@article{brown_2023, title={Singular Lagrangians and the Dirac-Bergmann algorithm in classical mechanics}, volume={91}, ISSN={["1943-2909"]}, url={http://inspirehep.net/record/2636260}, DOI={10.1119/5.0107540}, abstractNote={Textbook treatments of classical mechanics typically assume that the Lagrangian is nonsingular; that is, the matrix of second derivatives of the Lagrangian with respect to the velocities is invertible. This assumption ensures that (i) Lagrange's equations can be solved for the accelerations as functions of coordinates and velocities, and (ii) the definitions of the conjugate momenta can be inverted to solve for the velocities as functions of coordinates and momenta. This assumption, however, is unnecessarily restrictive—there are interesting classical dynamical systems with singular Lagrangians. The algorithm for analyzing such systems was developed by Dirac and Bergmann in the 1950s. After a brief review of the Dirac–Bergmann algorithm, several examples are presented using familiar components: point masses connected by massless springs, rods, cords, and pulleys.}, number={3}, journal={AMERICAN JOURNAL OF PHYSICS}, author={Brown, J. David}, year={2023}, month={Mar}, pages={214–224} }
@article{waldstein_brown_2022, title={Generalized geodesic deviation in de Sitter spacetime}, volume={39}, ISSN={["1361-6382"]}, url={http://inspirehep.net/record/1984845}, DOI={10.1088/1361-6382/ac6a9e}, abstractNote={Abstract The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The GDE assumes that nearby geodesics have a small rate of separation, which is formally treated as the same order in smallness as the separation itself. This assumption is discussed in various papers but is not articulated in any standard textbooks on general relativity. Relaxing this assumption leads to the generalized geodesic deviation equation (GGDE). We elucidate the distinction between the GDE and the GGDE by explicitly computing the relative acceleration between timelike geodesics in two–dimensional de Sitter spacetime. We do this by considering a ﬁducial geodesic and a secondary geodesic (both timelike) that cross with nonzero speed. These geodesics are spanned by a spacelike geodesic, whose tangent evaluated at the ﬁducial geodesic deﬁnes the separation. The second derivative of the separation describes the relative acceleration between the ﬁducial and secondary geodesics. Near the crossing point, where the separation between the timelike geodesics is small but their rates of separation can be large, we show that the GGDE holds but the GDE fails to apply.}, number={11}, journal={CLASSICAL AND QUANTUM GRAVITY}, author={Waldstein, Isaac Raj and Brown, J. David}, year={2022}, month={Jun} }
@article{brown_2022, title={Singular Lagrangians, Constrained Hamiltonian Systems and Gauge Invariance: An Example of the Dirac-Bergmann Algorithm}, volume={8}, ISSN={["2218-1997"]}, url={https://www.mdpi.com/2218-1997/8/3/171}, DOI={10.3390/universe8030171}, abstractNote={The Dirac-Bergmann algorithm is a recipe for converting a theory with a singular Lagrangian into a constrained Hamiltonian system. Constrained Hamiltonian systems include gauge theories -- general relativity, electromagnetism, Yang Mills, string theory, etc. The Dirac-Bergmann algorithm is elegant but at the same time rather complicated. It consists of a large number of logical steps linked together by a subtle chain of reasoning. Examples of the Dirac-Bergmann algorithm found in the literature are designed to isolate and illustrate just one or two of those logical steps. In this paper I analyze a finite-dimensional system that exhibits all of the major steps in the algorithm. The system includes primary and secondary constraints, first and second class constraints, restrictions on Lagrange multipliers, and both physical and gauge degrees of freedom. This relatively simple system provides a platform for discussing the Dirac conjecture, constructing Dirac brackets, and applying gauge conditions.}, number={3}, journal={UNIVERSE}, author={Brown, J. David}, year={2022}, month={Mar} }
@article{brown_2021, title={Elasticity theory in general relativity}, volume={38}, ISBN={1361-6382}, url={http://inspirehep.net/record/1790455}, DOI={10.1088/1361-6382/abe1ff}, abstractNote={The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. The equations of motion and stress-energy-momentum tensor for a hyperelastic body are derived from the gauge-invariant action principle first considered by DeWitt. This action is a natural extension of the action for a single relativistic particle. The central object in the Lagrangian treatment is the Landau-Lifshitz radar metric, which is the relativistic version of the right Cauchy-Green deformation tensor. We also introduce relativistic definitions of the deformation gradient, Green strain, and first and second Piola-Kirchhoff stress tensors. A gauge-fixed description of relativistic hyperelasticity is also presented, and the nonrelativistic theory is derived in the limit as the speed of light becomes infinite.}, number={8}, journal={Classical and Quantum Gravity}, author={Brown, J. David}, year={2021}, pages={085017} }
@article{loomis_brown_2017, title={Continuous body dynamics and the Mathisson-Papapetrou-Dixon equations}, volume={95}, url={http://inspirehep.net/record/1507990}, DOI={10.1103/PhysRevD.95.044025}, abstractNote={We show that an effective particle Lagrangian yields the Mathisson-Papapetrou-Dixon (MPD) equations. The spin of the effective particle is defined without any reference to a fixed body frame or angular velocity variable. We then demonstrate that a continuous body, defined by a congruence of world lines and described by a general action, can be rewritten as an effective particle. We analyze the gauge freedom of the body and show that a natural center of mass condition is related to a spin supplementary condition.}, number={4}, journal={Phys.Rev.D}, author={Loomis, S.P. and Brown, John}, year={2017}, month={Feb}, pages={044025} }
@article{brown_diener_field_hesthaven_herrmann_mroue_sarbach_schnetter_tiglio_wagman_2012, title={Numerical simulations with a first order BSSN formulation of Einstein's field equations}, volume={85}, url={http://inspirehep.net/record/1087884}, DOI={10.1103/PhysRevD.85.084004}, abstractNote={We present a new fully first-order strongly hyperbolic representation of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyperbolicity properties, and present two numerical implementations and simulations: one using finite differences, adaptive mesh refinement, and, in particular, binary black holes, and another one using the discontinuous Galerkin method in spherical symmetry. The results of this paper constitute a first step in an effort to combine the robustness of Baumgarte-Shapiro-Shibata-Nakamura evolutions with very high accuracy numerical techniques, such as spectral collocation multidomain or discontinuous Galerkin methods.}, journal={Phys.Rev.D}, author={Brown, J.David and Diener, Peter and Field, Scott E. and Hesthaven, Jan S. and Herrmann, Frank and Mroue, Abdul H. and Sarbach, Olivier and Schnetter, Erik and Tiglio, Manuel and Wagman, Michael}, year={2012}, pages={084004} }
@article{brown_2011, title={Action Principle for the Generalized Harmonic Formulation of General Relativity}, volume={84}, url={http://inspirehep.net/record/865737}, DOI={10.1103/PhysRevD.84.084014}, abstractNote={An action principle for the generalized harmonic formulation of general relativity is presented. The action is a functional of the spacetime metric and the gauge source vector. An action principle for the Z4 formulation of general relativity has been proposed recently by Bona, Bona--Casas and Palenzuela (BBP). The relationship between the generalized harmonic action and the BBP action is discussed in detail.}, journal={Phys.Rev.D}, author={Brown, J.David}, year={2011}, pages={084014} }
@article{brown_2011, title={Generalized Harmonic Equations in 3+1 Form}, volume={84}, url={http://inspirehep.net/record/926739}, DOI={10.1103/PhysRevD.84.124012}, abstractNote={The generalized harmonic equations of general relativity are written in $3+1$ form. The result is a system of partial differential equations with first-order time and second-order space derivatives for the spatial metric, extrinsic curvature, lapse function and shift vector, plus fields that represent the time derivatives of the lapse and shift. This allows for a direct comparison between the generalized harmonic and the Arnowitt-Deser-Misner formulations. The $3+1$ generalized harmonic equations are also written in terms of conformal variables and compared to the Baumgarte-Shapiro-Shibata-Nakamura equations with moving puncture gauge conditions.}, journal={Phys.Rev.D}, author={Brown, J.David}, year={2011}, pages={124012} }
@article{staley_baumgarte_brown_farris_shapiro_2011, title={Oppenheimer–Snyder collapse in moving-puncture coordinates}, volume={29}, ISSN={0264-9381 1361-6382}, url={http://dx.doi.org/10.1088/0264-9381/29/1/015003}, DOI={10.1088/0264-9381/29/1/015003}, abstractNote={Moving-puncture coordinates are commonly used in numerical simulations of black holes. Their properties for vacuum Schwarzschild black holes have been analyzed in a number of studies. The behavior of moving-puncture coordinates in spacetimes containing matter, however, is less well understood. In this paper we explore the behavior of these coordinates for Oppenheimer-Snyder collapse, i.e., the collapse of a uniform density, pressureless sphere of dust initially at rest to a black hole. Oppenheimer-Snyder collapse provides a stringent test of the singularity-avoiding properties of moving-puncture coordinates, since the singularity can form more quickly than it would for matter with pressure. Our results include analytical expressions for the matter density, lapse function, and mean curvature at early times, as well as interesting limits for later times. We also carry out numerical simulations to obtain the full solution and these show that, even in the absence of pressure, moving-puncture coordinates are able to avoid the singularity. At late times the geometry settles down to a trumpet slice of a vacuum black hole.}, number={1}, journal={Classical and Quantum Gravity}, publisher={IOP Publishing}, author={Staley, A N and Baumgarte, T W and Brown, J D and Farris, B and Shapiro, S L}, year={2011}, month={Dec}, pages={015003} }
@article{dennison_wendell_baumgarte_brown_2010, title={Trumpet slices of the Schwarzschild-Tangherlini spacetime}, volume={82}, url={http://inspirehep.net/record/874598}, DOI={10.1103/PhysRevD.82.124057}, abstractNote={We study families of time-independent maximal and $1+\mathrm{log}$ foliations of the Schwarzschild-Tangherlini spacetime, the spherically symmetric vacuum black hole solution in $D$ spacetime dimensions, for $D\ensuremath{\ge}4$. We identify special members of these families for which the spatial slices display a trumpet geometry. Using a generalization of the $1+\mathrm{log}$ slicing condition that is parameterized by a constant $n$ we recover the results of Nakao, Abe, Yoshino, and Shibata in the limit of maximal slicing. We also construct a numerical code that evolves the Baumgarte-Shapiro-Shibata-Nakamura equations for $D=5$ in spherical symmetry using moving-puncture coordinates and demonstrate that these simulations settle down to the trumpet solutions.}, journal={Phys.Rev.D}, author={Dennison, Kenneth A. and Wendell, John P. and Baumgarte, Thomas W. and Brown, J.David}, year={2010}, pages={124057} }
@article{brown_2009, title={Covariant formulations of BSSN and the standard gauge}, volume={79}, url={http://inspirehep.net/record/813874}, DOI={10.1103/PhysRevD.79.104029}, abstractNote={The Baumgarte-Shapiro-Shibata-Nakamura (BSSN) and standard gauge equations are written in covariant form with respect to spatial coordinate transformations. The BSSN variables are defined as tensors with no density weights. This allows us to evolve a given set of initial data using two different coordinate systems and to relate the results using the familiar tensor transformation rules. Two variants of the covariant equations are considered. These differ from one another in the way that the determinant of the conformal metric is evolved.}, journal={Phys.Rev.D}, author={Brown, J.David}, year={2009}, pages={104029} }
@article{brown_2009, title={Probing the puncture for black hole simulations}, volume={80}, ISSN={["1550-2368"]}, url={http://inspirehep.net/record/829536}, DOI={10.1103/PhysRevD.80.084042}, abstractNote={With the puncture method for black hole simulations, the second infinity of a wormhole geometry is compactified to a single ``puncture point'' on the computational grid. The region surrounding the puncture quickly evolves to a trumpet geometry. The computational grid covers only a portion of the trumpet throat. It ends at a boundary whose location depends on resolution. This raises the possibility that perturbations in the trumpet geometry could propagate down the trumpet throat, reflect from the puncture boundary, and return to the black hole exterior with a resolution-dependent time delay. Such pathological behavior is not observed. This is explained by the observation that some perturbative modes propagate in the conformal geometry, others propagate in the physical geometry. The puncture boundary exists only in the physical geometry. The modes that propagate in the physical geometry are always directed away from the computational domain at the puncture boundary. The finite difference stencils ensure that these modes are advected through the boundary with no coupling to the modes that propagate in the conformal geometry. These results are supported by numerical experiments with a code that evolves spherically symmetric gravitational fields with standard Cartesian finite difference stencils. The code uses the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations with $1+\mathrm{log}$ slicing and gamma-driver shift conditions.}, number={8}, journal={PHYSICAL REVIEW D}, author={Brown, J. David}, year={2009}, month={Oct} }
@inproceedings{brown_2009, title={Strongly Hyperbolic Extensions of the ADM Hamiltonian}, url={http://inspirehep.net/record/780593}, DOI={10.1007/978-0-387-87499-9_6}, abstractNote={The ADM Hamiltonian formulation of general relativity with prescribed lapse and shift is a weakly hyperbolic system of partial differential equations. In general weakly hyperbolic systems are not mathematically well posed. For well posedness, the theory should be reformulated so that the complete system, evolution equations plus gauge conditions, is (at least) strongly hyperbolic. Traditionally, reformulation has been carried out at the level of equations of motion. This typically destroys the variational and Hamiltonian structures of the theory. Here I show that one can extend the ADM formalism to (i) incorporate the gauge conditions as dynamical equations and (ii) affect the hyperbolicity of the complete system, all while maintaining a Hamiltonian description. The extended ADM formulation is used to obtain a strongly hyperbolic Hamiltonian description of Einstein's theory that is generally covariant under spatial diffeomorphisms and time reparametrizations, and has physical characteristics. The extended Hamiltonian formulation with 1+log slicing and gamma--driver shift conditions is weakly hyperbolic.}, booktitle={workshop on Quantum Mechanics of Fundamental Systems: the Quest for Beauty and Simplicity: Dedicated to Claudio Bunster on the occasion of his 60th birthday}, author={Brown, J.David}, year={2009}, pages={71–90} }
@article{brown_diener_sarbach_schnetter_tiglio_2009, title={Turduckening black holes: An analytical and computational study}, volume={79}, ISSN={["1550-2368"]}, url={http://inspirehep.net/record/797151}, DOI={10.1103/physrevd.79.044023}, abstractNote={We provide a detailed analysis of several aspects of the turduckening technique for evolving black holes. At the analytical level we study the constraint propagation for a general family of BSSN-type formulation of Einstein's field equations and identify under what conditions the turducken procedure is rigorously justified and under what conditions constraint violations will propagate to the outside of the black holes. We present high-resolution spherically symmetric studies which verify our analytical predictions. Then we present three dimensional simulations of single distorted black holes using different variations of the turduckening method and also the puncture method. We study the effect that these different methods have on the coordinate conditions, constraint violations, and extracted gravitational waves. We find that the waves agree up to small but non-vanishing differences, caused by escaping superluminal gauge modes. These differences become smaller with increasing detector location.}, number={4}, journal={PHYSICAL REVIEW D}, author={Brown, David and Diener, Peter and Sarbach, Olivier and Schnetter, Erik and Tiglio, Manuel}, year={2009}, month={Feb} }
@article{brown_2008, title={BSSN in spherical symmetry}, volume={25}, ISSN={["1361-6382"]}, url={http://inspirehep.net/record/751519}, DOI={10.1088/0264-9381/25/20/205004}, abstractNote={The BSSN (Baumgarte?Shapiro?Shibata?Nakamura) formulation of the Einstein evolution equations is written in spherical symmetry. These equations can be used to address a number of technical and conceptual issues in numerical relativity in the context of a single Schwarzschild black hole. One of the benefits of spherical symmetry is that the numerical grid points can be tracked on a Kruskal?Szekeres diagram. Boundary conditions suitable for puncture evolution of a Schwarzschild black hole are presented. Several results are shown for puncture evolution using a fourth-order finite difference implementation of the equations.}, number={20}, journal={CLASSICAL AND QUANTUM GRAVITY}, author={Brown, J. David}, year={2008}, month={Oct} }
@article{brown_2008, title={Puncture Evolution of Schwarzschild Black Holes}, volume={77}, url={http://inspirehep.net/record/750274}, DOI={10.1103/PhysRevD.77.044018}, abstractNote={The moving puncture method is analyzed for a single, nonspinning black hole. It is shown that the puncture region is not resolved by current numerical codes. As a result, the geometry near the puncture appears to evolve to an infinitely long cylinder of finite areal radius. The puncture itself actually remains at spacelike infinity throughout the evolution. In the limit of infinite resolution the data never become stationary. However, at any reasonable finite resolution the grid points closest to the puncture are rapidly drawn into the black hole interior by the {gamma}-driver shift condition. The data can then evolve to a stationary state. These results suggest that the moving puncture technique should be viewed as a type of ''natural excision.''.}, journal={Phys.Rev.D}, author={Brown, J.David}, year={2008}, pages={044018} }
@article{brown_sarbach_schnetter_tiglio_diener_hawke_pollney_2007, title={Excision without excision}, volume={76}, ISSN={["2470-0029"]}, url={http://inspirehep.net/record/756370}, DOI={10.1103/physrevd.76.081503}, abstractNote={to turducken (turduckens, turduckening, turduckened, turduckened) [math.]: To stuff a black hole. We analyze and apply an alternative to black hole excision based on smoothing the interior of black holes with arbitrary initial data, and solving the vacuum Einstein evolution equations everywhere. By deriving the constraint propagation system for our hyperbolic formulation of the BSSN evolution system we rigorously prove that the constraints propagate causally and so any constraint violations introduced inside the black holes cannot affect the exterior spacetime. We present evolutions of Cook-Pfeiffer binary black hole initial configurations showing that these techniques appear to work robustly for generic data. We also present evidence from spherically symmetric evolutions that for the gauge conditions used the same stationary end-state is approached irrespective of the choice of initial data and smoothing procedure.}, number={8}, journal={PHYSICAL REVIEW D}, author={Brown, David and Sarbach, Olivier and Schnetter, Erik and Tiglio, Manuel and Diener, Peter and Hawke, Ian and Pollney, Denis}, year={2007}, month={Oct} }
@article{brown_2006, title={Midpoint rule as a variational-symplectic integrator: Hamiltonian systems}, volume={73}, ISSN={["1550-2368"]}, url={http://inspirehep.net/record/696937}, DOI={10.1103/physrevd.73.024001}, abstractNote={Numerical algorithms based on variational and symplectic integrators exhibit special features that make them promising candidates for application to general relativity and other constrained Hamiltonian systems. This paper lays part of the foundation for such applications. The midpoint rule for Hamilton's equations is examined from the perspectives of variational and symplectic integrators. It is shown that the midpoint rule preserves the symplectic form, conserves Noether charges, and exhibits excellent long--term energy behavior. The energy behavior is explained by the result, shown here, that the midpoint rule exactly conserves a phase space function that is close to the Hamiltonian. The presentation includes several examples.}, number={2}, journal={PHYSICAL REVIEW D}, author={Brown, JD}, year={2006}, month={Jan} }
@article{brown_lowe_2006, title={Modifying the Einstein equations off the constraint hypersurface}, volume={74}, ISSN={["2470-0029"]}, url={http://inspirehep.net/record/718410}, DOI={10.1103/physrevd.74.104023}, abstractNote={A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the gravitational field variables are modified by the addition of terms that are linear and nonlocal in the constraints. These terms are obtained from solutions of the linearized Einstein constraints.}, number={10}, journal={PHYSICAL REVIEW D}, author={Brown, J. David and Lowe, Lisa L.}, year={2006}, month={Nov} }
@article{brown_2005, title={Conformal invariance and the conformal-traceless decomposition of the gravitational field}, volume={71}, ISSN={["1550-2368"]}, url={http://inspirehep.net/record/675752}, DOI={10.1103/physrevd.71.104011}, abstractNote={Einstein's theory of general relativity is written in terms of the variables obtained from a conformal--traceless decomposition of the spatial metric and extrinsic curvature. The determinant of the conformal metric is not restricted, so the action functional and equations of motion are invariant under conformal transformations. With this approach the conformal--traceless variables remain free of density weights. The conformal invariance of the equations of motion can be broken by imposing an evolution equation for the determinant of the conformal metric g. Two conditions are considered, one in which g is constant in time and one in which g is constant along the unit normal to the spacelike hypersurfaces. This approach is used to write the Baumgarte--Shapiro--Shibata--Nakamura system of evolution equations in conformally invariant form. The presentation includes a discussion of the conformal thin sandwich construction of gravitational initial data, and the conformal flatness condition as an approximation to the evolution equations.}, number={10}, journal={PHYSICAL REVIEW D}, author={Brown, JD}, year={2005}, month={May} }
@article{brown_lowe_2005, title={Multigrid elliptic equation solver with adaptive mesh refinement}, volume={209}, ISSN={["1090-2716"]}, url={http://inspirehep.net/record/665142}, DOI={10.1016/j.jcp.2005.03.026}, abstractNote={In this paper we describe in detail the computational algorithm used by our parallel multigrid elliptic equation solver with adaptive mesh refinement. Our code uses truncation error estimates to adaptively refine the grid as part of the solution process. The presentation includes a discussion of the orders of accuracy that we use for prolongation and restriction operators to ensure second order accurate results and to minimize computational work. Code tests are presented that confirm the overall second order accuracy and demonstrate the savings in computational resources provided by adaptive mesh refinement.}, number={2}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Brown, JD and Lowe, LL}, year={2005}, month={Nov}, pages={582–598} }
@article{brown_lowe_2004, title={Distorted black hole initial data using the puncture method}, volume={70}, ISSN={["1550-2368"]}, url={http://inspirehep.net/record/657537}, DOI={10.1103/physrevd.70.124014}, abstractNote={We solve for single distorted black hole initial data using the puncture method, where the Hamiltonian constraint is written as an elliptic equation in R^3 for the nonsingular part of the metric conformal factor. With this approach we can generate isometric and non--isometric black hole data. For the isometric case, our data are directly comparable to those obtained by Bernstein et al., who impose isometry boundary conditions at the black hole throat. Our numerical simulations are performed using a parallel multigrid elliptic equation solver with adaptive mesh refinement. Mesh refinement allows us to use high resolution around the black hole while keeping the grid boundaries far away in the asymptotic region.}, number={12}, journal={PHYSICAL REVIEW D}, author={Brown, JD and Lowe, LL}, year={2004}, month={Dec} }
@article{imbiriba_baker_choi_centrella_fiske_brown_meter_olson_2004, title={Evolving a puncture black hole with fixed mesh refinement}, volume={70}, ISSN={["1550-2368"]}, url={http://inspirehep.net/record/646211}, DOI={10.1103/physrevd.70.124025}, abstractNote={We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular attention to the convergence properties of the simulations. In our applications of this technique to the evolution of puncture initial data with vanishing shift, we demonstrate that it is possible to simultaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult and wave extraction is meaningful.}, number={12}, journal={PHYSICAL REVIEW D}, author={Imbiriba, B and Baker, J and Choi, DI and Centrella, J and Fiske, DR and Brown, JD and Meter, JR and Olson, K}, year={2004}, month={Dec} }
@article{choi_brown_imbiriba_centrella_macneice_2004, title={Interface conditions for wave propagation through mesh refinement boundaries}, volume={193}, ISSN={["1090-2716"]}, url={http://inspirehep.net/record/625478}, DOI={10.1016/j.jcp.2003.07.036}, abstractNote={We study the propagation of waves across fixed mesh refinement boundaries in linear and nonlinear model equations in 1--D and 2--D, and in the 3--D Einstein equations of general relativity. We demonstrate that using linear interpolation to set the data in guard cells leads to the production of reflected waves at the refinement boundaries. Implementing quadratic interpolation to fill the guard cells suppresses these spurious signals.}, number={2}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Choi, DI and Brown, JD and Imbiriba, B and Centrella, J and MacNeice, P}, year={2004}, month={Jan}, pages={398–425} }
@article{brown_lau_york_2002, title={Action and energy of the gravitational field}, volume={297}, ISSN={["0003-4916"]}, DOI={10.1006/aphy.2002.6250}, abstractNote={Abstract We present a detailed examination of the variational principle for metric general relativity as applied to a quasilocal spacetime region M (that is, a region that is both spatially and temporally bounded). Our analysis relies on the Hamiltonian formulation of general relativity and thereby assumes a foliation of M into spacelike hypersurfaces Σ. We allow for near complete generality in the choice of foliation. Using a field-theoretic generalization of Hamilton–Jacobi theory, we define the quasilocal stress-energy momentum of the gravitational field by varying the action with respect to the metric on the boundary ∂ M . The gravitational stress-energy momentum is defined for a two-surface B spanned by a spacelike hypersurface in spacetime. We examine the behavior of the gravitational stress-energy momentum under boosts of the spanning hypersurface. The boost relations are derived from the geometrical and invariance properties of the gravitational action and Hamiltonian. Finally, we present several new examples of quasilocal energy momentum, including a novel discussion of quasilocal energy momentum in the large-sphere limit toward spatial infinity.}, number={2}, journal={ANNALS OF PHYSICS}, author={Brown, JD and Lau, SR and York, JW}, year={2002}, month={May}, pages={175–218} }
@article{centrella_new_lowe_brown_2001, title={Dynamical rotational instability at low T/W}, volume={550}, ISSN={["0004-637X"]}, url={http://inspirehep.net/record/551720}, DOI={10.1086/319634}, abstractNote={Dynamical instability is shown to occur in differentially rotating polytropes with N = 3.33 and $T/|W| \gtrsim 0.14$. This instability has a strong m=1 mode, although the m=2, 3, and 4 modes also appear. Such instability may allow a centrifugally-hung core to begin collapsing to neutron star densities on a dynamical timescale. The gravitational radiation emitted by such unstable cores may be detectable with advanced ground-based detectors, such as LIGO II. If the instability occurs in a supermassive star, it may produce gravitational radiation detectable by the space-based detector LISA.}, number={2}, journal={ASTROPHYSICAL JOURNAL}, author={Centrella, JM and New, KCB and Lowe, LL and Brown, JD}, year={2001}, month={Apr}, pages={L193–L196} }
@inproceedings{brown_2001, title={Rotational instabilities in post collapse stellar cores}, volume={575}, ISBN={0735400148}, url={http://inspirehep.net/record/516336}, DOI={10.1063/1.1387315}, abstractNote={A core–collapse supernova might produce large amplitude gravitational waves if, through the collapse process, the inner core can aquire enough rotational energy to become dynamically unstable. In this report I present the results of 3-D numerical simulations of core collapse supernovae. These simulations indicate that for some initial conditions the post–collapse inner core is indeed unstable. However, for the cases considered, the instability does not produce a large gravitational–wave signal.}, number={1}, booktitle={Astrophysical sources for ground based gravitational wave detectors}, publisher={Melville, NY: American Institute of Physics}, author={Brown, J. D.}, editor={Centrella, J. M.Editor}, year={2001}, pages={234–245} }
@article{brown_lau_york_2000, title={Action and energy of the gravitational field}, volume={10}, url={http://inspirehep.net/record/534655}, author={Brown, J.David and Lau, S.R. and York, James W., Jr.}, year={2000}, month={Oct} }
@article{brown_2000, title={Gravitational waves from the dynamical bar instability in a rapidly rotating star}, volume={62}, ISSN={["2470-0029"]}, url={http://inspirehep.net/record/525689}, DOI={10.1103/physrevd.62.084024}, abstractNote={A rapidly rotating, axisymmetric star can be dynamically unstable to an $m=2$ ``bar'' mode that transforms the star from a disk shape to an elongated bar. The fate of such a bar-shaped star is uncertain. Some previous numerical studies indicate that the bar is short lived, lasting for only a few bar-rotation periods, while other studies suggest that the bar is relatively long lived. This paper contains the results of a numerical simulation of a rapidly rotating $\ensuremath{\gamma}=5/3$ fluid star. The simulation shows that the bar shape is long lived: once the bar is established, the star retains this shape for more than 10-bar-rotation periods, through the end of the simulation. The results are consistent with the conjecture that a star will retain its bar shape indefinitely on a dynamical time scale, as long as its rotation rate exceeds the threshold for secular bar instability. The results are described in terms of a low-density neutron star, but can be scaled to represent, for example, a burned-out stellar core that is prevented from complete collapse by centrifugal forces. Estimates for the gravitational-wave signal indicate that a dynamically unstable neutron star in our galaxy can be detected easily by the first generation of ground based gravitational-wave detectors. The signal for an unstable neutron star in the Virgo cluster might be seen by the planned advanced detectors. The Newtonian-quadrupole approximation is used throughout this work.}, number={8}, journal={PHYSICAL REVIEW D}, author={Brown, JD}, year={2000}, month={Oct} }
@article{brown_lau_york_1999, title={Canonical quasilocal energy and small spheres}, volume={59}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/477238}, DOI={10.1103/physrevd.59.064028}, abstractNote={Consider the definition E of quasilocal energy stemming from the Hamilton-Jacobi method as applied to the canonical form of the gravitational action. We examine E in the standard "small-sphere limit," first considered by Horowitz and Schmidt in their examination of Hawking's quasilocal mass. By the term "small sphere" we mean a cut S(r), level in an affine radius r, of the lightcone belonging to a generic spacetime point. As a power series in r, we compute the energy E of the gravitational and matter fields on a spacelike hypersurface spanning S(r). Much of our analysis concerns conceptual and technical issues associated with assigning the zero-point of the energy. For the small-sphere limit, we argue that the correct zero-point is obtained via a "lightcone reference," which stems from a certain isometric embedding of S(r) into a genuine lightcone of Minkowski spacetime. Choosing this zero-point, we find agreement with Hawking's quasilocal mass expression, up to and including the first non-trivial order in the affine radius. The vacuum limit relates the quasilocal energy directly to the Bel-Robinson tensor.}, number={6}, journal={PHYSICAL REVIEW D}, author={Brown, JD and Lau, SR and York, JW}, year={1999}, month={Mar} }
@article{brown_1998, title={Boundary states and black hole entropy}, volume={57}, ISSN={["2470-0029"]}, url={http://inspirehep.net/record/442542}, DOI={10.1103/physrevd.57.2624}, abstractNote={Black hole entropy is derived from a sum over boundary states. The boundary states are labeled by energy and momentum surface densities, and parametrized by the boundary metric. The sum over state labels is expressed as a functional integral with measure determined by the density of states. The sum over metrics is expressed as a functional integral with measure determined by the universal expression for the inverse temperature gradient at the horizon. The analysis applies to any stationary, nonextreme black hole in any theory of gravitational and matter fields.}, number={4}, journal={PHYSICAL REVIEW D}, author={Brown, JD}, year={1998}, month={Feb}, pages={2624–2627} }
@inproceedings{brown_1998, title={Commentary on Lanczos's 'Remark on the de Sitter universe'}, ISBN={0929493003}, booktitle={Cornelius Lanczos collected published papers with commentaries}, publisher={Raleigh: College of Physical and Mathematical Sciences, North Carolina State University}, author={Brown, J. D.}, year={1998}, pages={2–41} }
@inproceedings{brown_1998, title={Commentary on Lanczos's 'Surface distribution of matter in Einstein's theory of gravitation'}, ISBN={0929493003}, booktitle={Cornelius Lanczos collected published papers with commentaries}, publisher={Raleigh: College of Physical and Mathematical Sciences, North Carolina State University}, author={Brown, J. D.}, year={1998}, pages={2/264–2265} }
@inproceedings{brown_york_1998, title={path integral formulation of gravitational thermodynamics}, ISBN={9810233418}, DOI={10.1142/9789814447232_0001}, booktitle={The black hole 25 years after}, publisher={Singapore: World Scientific}, author={Brown, J. D. and York, J. W.}, editor={C. Teitelboim and Zanelli, J.Editors}, year={1998}, pages={1–24} }
@article{brown_husain_1997, title={Black holes with short hair}, volume={6}, url={http://inspirehep.net/record/445594}, DOI={10.1142/s0218271897000340}, abstractNote={We present spherically symmetric black hole solutions for Einstein gravity coupled to anisotropic matter. We show that these black holes have arbitrarily short hair, and argue for stability by showing that they can arise from dynamical collapse. We also show that a recent `no short hair' theorem does not apply to these solutions.}, number={5}, journal={International Journal of Modern Physics. D, Gravitation, Astrophysics, Cosmology}, author={Brown, J. D. and Husain, V.}, year={1997}, pages={563–573} }
@article{brown_1997, title={Duality invariance of black hole creation rates}, volume={56}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/440617}, DOI={10.1103/physrevd.56.1001}, abstractNote={Pair creation of electrically charged black holes and its dual process, pair creation of magnetically charged black holes, are considered. It is shown that the creation rates are equal provided the boundary conditions for the two processes are dual to one another. This conclusion follows from a careful analysis of boundary terms and boundary conditions for the Maxwell action.}, number={2}, journal={PHYSICAL REVIEW D}, author={Brown, JD}, year={1997}, month={Jul}, pages={1001–1004} }
@article{brown_lau_york_1997, title={Energy of isolated systems at retarded times as the null limit of quasilocal energy}, volume={55}, ISSN={["2470-0029"]}, url={http://inspirehep.net/record/423731}, DOI={10.1103/physrevd.55.1977}, abstractNote={We define the energy of a perfectly isolated system at a given retarded time as the suitable null limit of the quasilocal energy $E$. The result coincides with the Bondi-Sachs mass. Our $E$ is the lapse-unity shift-zero boundary value of the gravitational Hamiltonian appropriate for the partial system $\ensuremath{\Sigma}$ contained within a finite topologically spherical boundary $B=\ensuremath{\partial}\ensuremath{\Sigma}$. Moreover, we show that with an arbitrary lapse and zero shift the same null limit of the Hamiltonian defines a physically meaningful element in the space dual to supertranslations. This result is specialized to yield an expression for the full Bondi-Sachs four-momentum in terms of Hamiltonian values.}, number={4}, journal={PHYSICAL REVIEW D}, author={Brown, JD and Lau, SR and York, JW}, year={1997}, month={Feb}, pages={1977–1984} }
@article{brown_1996, title={On variational principles for gravitating perfect fluids}, volume={248}, DOI={10.1006/aphy.1996.0049}, abstractNote={The connection is established between two different action principles for perfect fluids in the context of general relativity. For one of these actions, S , the fluid four–velocity is expressed as a sum of products of scalar fields and their gradients (the velocity–potential representation). For the other action, S , the fluid four–velocity is proportional to the totally antisymmetric product of gradients of the fluid Lagrangian coordinates. The relationship between S and S is established by expressing S in Hamiltonian form and identifying certain canonical coordinates as ignorable. Elimination of these coordinates and their conjugates yields the action S . The key step in the analysis is a point canonical transformation in which all tensor fields on space are expressed in terms of the Lagrangian coordinate system supplied by the fluid. The canonical transformation is of interest in its own right. It can be applied to any physical system that includes a material medium described by Lagrangian coordinates. The result is a Hamiltonian description of the system in which the momentum constraint is trivial.}, journal={Annals of Physics}, author={Brown, J. D.}, year={1996}, pages={1–33} }
@article{brown_marolf_1996, title={Relativistic material reference systems}, volume={53}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/399454}, DOI={10.1103/physrevd.53.1835}, abstractNote={This work closes certain gaps in the literature on material reference systems in general relativity. It is shown that perfect fluids are a special case of DeWitt's relativistic elastic media and that the velocity--potential formalism for perfect fluids can be interpreted as describing a perfect fluid coupled to a fleet of clocks. A Hamiltonian analysis of the elastic media with clocks is carried out and the constraints that arise when the system is coupled to gravity are studied. When the Hamiltonian constraint is resolved with respect to the clock momentum, the resulting true Hamiltonian is found to be a functional only of the gravitational variables. The true Hamiltonian is explicitly displayed when the medium is dust, and is shown to depend on the detailed construction of the clocks.}, number={4}, journal={PHYSICAL REVIEW D}, author={Brown, JD and Marolf, D}, year={1996}, month={Feb}, pages={1835–1844} }
@article{brown_1995, title={BLACK-HOLE PAIR CREATION AND THE ENTROPY FACTOR}, volume={51}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/381115}, DOI={10.1103/physrevd.51.5725}, abstractNote={It is shown that in the instanton approximation the rate of creation of black holes is always enhanced by a factor of the exponential of the black hole entropy relative to the rate of creation of compact matter distributions (stars). This result holds for any generally covariant theory of gravitational and matter fields that can be expressed in Hamiltonian form. It generalizes the result obtained previously for the pair creation of magnetically charged black holes by a magnetic field in Einstein-Maxwell theory. The particular example of pair creation of electrically charged black holes by an electric field in Einstein-Maxwell theory is discussed in detail.}, number={10}, journal={PHYSICAL REVIEW D}, author={BROWN, JD}, year={1995}, month={May}, pages={5725–5731} }
@article{brown_1995, title={Black hole entropy and the Hamiltonian formulation of diffeomorphism invariant theories}, volume={52}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/396783}, DOI={10.1103/physrevd.52.7011}, abstractNote={Path integral methods are used to derive a general expression for the entropy of a black hole in a diffeomorphism invariant theory. The result, which depends on the variational derivative of the Lagrangian with respect to the Riemann tensor, agrees with the result obtained from Noether charge methods by Iyer and Wald. The method used here is based on the direct expression of the density of states as a path integral (the microcanonical functional integral). The analysis makes crucial use of the Hamiltonian form of the action. An algorithm for placing the action of a diffeomorphism invariant theory in Hamiltonian form is presented. Other path integral approaches to the derivation of black hole entropy include the Hilbert action surface term method and the conical deficit angle method. The relationships between these path integral methods are presented.}, number={12}, journal={PHYSICAL REVIEW D}, author={Brown, JD}, year={1995}, month={Dec}, pages={7011–7026} }
@article{brown_kuchar_1995, title={DUST AS A STANDARD OF SPACE AND TIME IN CANONICAL QUANTUM-GRAVITY}, volume={51}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/376344}, DOI={10.1103/physrevd.51.5600}, abstractNote={The coupling of the metric to an incoherent dust introduces into spacetime a privileged dynamical reference frame and time foliation. The comoving coordinates of the dust particles and the proper time along the dust worldlines become canonical coordinates in the phase space of the system. The Hamiltonian constraint can be resolved with respect to the momentum that is canonically conjugate to the dust time. Formal imposition of the resolved constraint as an operator restriction on the quantum states yields a functional Schr\"odinger equation. The ensuing Hamiltonian density has an extraordinary feature: it depends only on the geometric variables, not on the dust coordinates or time. This has three important consequences. First, the functional Schr\"odinger equation can be solved by separating the dust time from the geometric variables. Second, disregarding the standard factor-ordering difficulties, the Hamiltonian densities strongly commute and therefore can be simultaneously defined by spectral analysis. Third, the standard constraint system of vacuum gravity is cast into a form in which it generates a true Lie algebra. The particles of dust introduce into space a privileged system of coordinates that allows the supermomentum constraint to be solved explicitly. The Schr\"odinger equation yields a formally conserved inner product that can be written in terms of either the instantaneous state functionals or the solutions of constraints. Gravitational observables admit a similar dual representation. Examples of observables are given, though neither the intrinsic metric nor the extrinsic curvature are observables. This comes as close as one can reasonably expect to a satisfactory phenomenological quantization scheme that is free of most of the problems of time.}, number={10}, journal={PHYSICAL REVIEW D}, author={BROWN, JD and KUCHAR, KV}, year={1995}, month={May}, pages={5600–5629} }
@inproceedings{brown_1994, title={Black hole thermodynamics in a box}, ISBN={0898713390}, booktitle={Proceedings of the Cornelius Lanczos International Centenary Conference}, publisher={Philadelphia: SIAM}, author={Brown, J. D.}, editor={J. D. Brown, M. T. Chu and D. C. Ellison and Plemmons, R. J.Editors}, year={1994}, pages={548–550} }
@article{brown_1994, title={Black hole thermodynamics in a box}, volume={4}, url={http://inspirehep.net/record/372580}, author={Brown, J.David}, year={1994}, month={Apr} }
@inproceedings{brown_york_1994, title={Microcanonical action and the entropy of a rotating black hole}, volume={15}, ISBN={0792325001}, url={http://inspirehep.net/record/34485}, DOI={10.1007/978-94-011-1938-2_3}, abstractNote={The authors have recently proposed a “microcanonical functional integral” representation of the density of quantum states of the gravitational field. The phase of this real-time functional integral is determined by a “microcanonical” or Jacobi action, the extrema of which are classical solutions at fixed total energy, not at fixed total time interval as in Hamilton’s action. This approach is fully general but is especially well suited to gravitating systems because for them the total energy can be fixed simply as a boundary condition on the gravitational field. In this paper we describe how to obtain Jacobi’s action for general relativity. We evaluate it for a certain complex metric associated with a rotating black hole and discuss the relation of the result to the density of states and to the entropy of the black hole.}, booktitle={Physics on manifolds: Proceedings of the international colloquium in honour of Yvonne Choquet-Bruhat, Paris, June 3-5, 1992}, publisher={Dordrecht: Kluwer}, author={Brown, J. D. and York, J. W.}, editor={Flato, M. and Kerner, R. and Lichnerowicz, A.Editors}, year={1994}, pages={23–34} }
@article{brown_1994, title={On variational principles for gravitating perfect fluids}, volume={7}, url={http://inspirehep.net/record/374738}, author={Brown, J.David}, year={1994}, month={Jul} }
@book{proceedings of the cornelius lanczos international centenary conference_1994, ISBN={0898713390}, DOI={10.1006/jath.1995.1104}, publisher={Philadelphia: SIAM}, year={1994} }
@inproceedings{brown_1994, title={Reference fluids as standards of space and time}, ISBN={0898713390}, booktitle={Proceedings of the Cornelius Lanczos International Centenary Conference}, publisher={Philadelphia: SIAM}, author={Brown, J. D.}, editor={J. D. Brown, M. T. Chu and D. C. Ellison and Plemmons, R. J.Editors}, year={1994}, pages={563–565} }
@article{brown_1994, title={Reference fluids as standards of space and time}, volume={4}, url={http://inspirehep.net/record/372581}, author={Brown, J.David}, year={1994}, month={Apr} }
@article{brown_creighton_mann_1994, title={TEMPERATURE, ENERGY, AND HEAT-CAPACITY OF ASYMPTOTICALLY ANTI-DE SITTER BLACK-HOLES}, volume={50}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/37910}, DOI={10.1103/physrevd.50.6394}, abstractNote={We investigate the thermodynamical properties of black holes in (3+1) and (2+1) dimensional Einstein gravity with a negative cosmological constant. In each case, the thermodynamic internal energy is computed for a finite spatial region that contains the black hole. The temperature at the boundary of this region is defined by differentiating the energy with respect to entropy, and is equal to the product of the surface gravity (divided by~$2\pi$) and the Tolman redshift factor for temperature in a stationary gravitational field. We also compute the thermodynamic surface pressure and, in the case of the (2+1) black hole, show that the chemical potential conjugate to angular momentum is equal to the proper angular velocity of the black hole with respect to observers who are at rest in the stationary time slices. In (3+1) dimensions, a calculation of the heat capacity reveals the existence of a thermodynamically stable black hole solution and a negative heat capacity instanton. This result holds in the limit that the spatial boundary tends to infinity only if the comological constant is negative; if the cosmological constant vanishes, the stable black hole solution is lost. In (2+1) dimensions, a calculation of the heat capacity reveals the existence of a thermodynamically stable black hole solution, but no negative heat capacity instanton.}, number={10}, journal={PHYSICAL REVIEW D}, author={BROWN, JD and CREIGHTON, J and MANN, RB}, year={1994}, month={Nov}, pages={6394–6403} }
@inproceedings{brown_york_1994, title={Temperature and time in the geometry of rotating black holes}, ISBN={0521433282}, booktitle={Physical origins of time asymmetry}, publisher={Cambridge: Cambridge University Press}, author={Brown, J. D. and York, J. W.}, editor={J. J. Halliwell, J. Perez-Mercader and Zurek, W.Editors}, year={1994}, pages={465–474} }
@inproceedings{brown_york_1994, title={The Path integral formulation of gravitational thermodynamics}, url={http://inspirehep.net/record/373302}, booktitle={The Black Hole 25 Years After}, author={Brown, J.David and York, James W., Jr.}, year={1994}, month={Jan}, pages={1–24} }
@article{brown_1993, title={ACTION FUNCTIONALS FOR RELATIVISTIC PERFECT FLUIDS}, volume={10}, ISSN={["0264-9381"]}, url={http://inspirehep.net/record/344634}, DOI={10.1088/0264-9381/10/8/017}, abstractNote={Action functionals describing relativistic perfect fluids are presented. Two of these actions apply to fluids whose equations of state are specified by giving the fluid energy density as a function of particle number density and entropy per particle. Other actions apply to fluids whose equations of state are specified in terms of other choices of dependent and independent fluid variables. Particular cases include actions for isentropic fluids and pressureless dust. The canonical Hamiltonian forms of these actions are derived, symmetries and conserved charges are identified, and the boundary value and initial value problems are discussed. As in previous works on perfect fluid actions, the action functionals considered here depend on certain Lagrange multipliers and Lagrangian coordinate fields. Particular attention is paid to the interpretations of these variables and to their relationships to the physical properties of the fluid.}, number={8}, journal={CLASSICAL AND QUANTUM GRAVITY}, author={BROWN, JD}, year={1993}, month={Aug}, pages={1579–1606} }
@article{brown_york_1993, title={Jacobi's action and the density of states}, volume={2}, url={http://inspirehep.net/record/34159}, author={Brown, J.David and York, James W., Jr.}, year={1993}, month={Feb} }
@inproceedings{brown_york_1993, title={Jacobi's action and the density of states}, ISBN={0521452678}, DOI={10.1017/cbo9780511524653.006}, booktitle={Directions in relativity: Proceedings of the 1993 symposium, Maryland}, publisher={Cambridge: Cambridge University Press}, author={Brown, J. D. and York, J. W.}, editor={B. L. Hu and Jacobson, T. A.Editors}, year={1993}, pages={28–37} }
@article{brown_york_1993, title={MICROCANONICAL FUNCTIONAL INTEGRAL FOR THE GRAVITATIONAL-FIELD}, volume={47}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/339133}, DOI={10.1103/physrevd.47.1420}, abstractNote={The gravitational field in a spatially finite region is described as a microcanonical system. The density of states $\nu$ is expressed formally as a functional integral over Lorentzian metrics and is a functional of the geometrical boundary data that are fixed in the corresponding action. These boundary data are the thermodynamical extensive variables, including the energy and angular momentum of the system. When the boundary data are chosen such that the system is described semiclassically by {\it any} real stationary axisymmetric black hole, then in this same approximation $\ln\nu$ is shown to equal 1/4 the area of the black hole event horizon. The canonical and grand canonical partition functions are obtained by integral transforms of $\nu$ that lead to "imaginary time" functional integrals. A general form of the first law of thermodynamics for stationary black holes is derived. For the simpler case of nonrelativistic mechanics, the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary-time functional integral for the canonical partition function.}, number={4}, journal={PHYSICAL REVIEW D}, author={BROWN, JD and YORK, JW}, year={1993}, month={Feb}, pages={1420–1431} }
@article{brown_york_1993, title={QUASI-LOCAL ENERGY AND CONSERVED CHARGES DERIVED FROM THE GRAVITATIONAL ACTION}, volume={47}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/339134}, DOI={10.1103/physrevd.47.1407}, abstractNote={The quasilocal energy of gravitational and matter fields in a spatially bounded region is obtained by employing a Hamilton-Jacobi analysis of the action functional. First, a surface stress-energy-momentum tensor is defined by the functional derivative of the action with respect to the three-metric on $^{3}$B, the history of the system's boundary. Energy surface density, momentum surface density, and spatial stress are defined by projecting the surface stress tensor normally and tangentially to a family of spacelike two-surfaces that foliate $^{3}$B. The integral of the energy surface density over such a two-surface B is the quasilocal energy associated with a spacelike three-surface \ensuremath{\Sigma} whose orthogonal intersection with $^{3}$B is the boundary B. The resulting expression for quasilocal energy is given in terms of the total mean curvature of the spatial boundary B as a surface embedded in \ensuremath{\Sigma}. The quasilocal energy is also the value of the Hamiltonian that generates unit magnitude proper-time translations on $^{3}$B in the timelike direction orthogonal to B. Conserved charges such as angular momentum are defined using the surface stress tensor and Killing vector fields on $^{3}$B. For spacetimes that are asymptotically flat in spacelike directions, the quasilocal energy and angular momentum defined here agree with the results of Arnowitt, Deser, and Misner in the limit that the boundary tends to spatial infinity. For spherically symmetric spacetimes, it is shown that the quasilocal energy has the correct Newtonian limit, and includes a negative contribution due to gravitational binding.}, number={4}, journal={PHYSICAL REVIEW D}, author={BROWN, JD and YORK, JW}, year={1993}, month={Feb}, pages={1407–1419} }
@inproceedings{brown_york_1992, title={Quasilocal energy in general relativity}, ISBN={0821851446}, DOI={10.1090/conm/132/1188439}, booktitle={Mathematical aspects of classical field theory}, publisher={Providence, RI: American Mathematical Society}, author={Brown, J. D. and York, J. W.}, editor={M. J. Gotay, J. E. Marsden and Moncrief, V. E.Editors}, year={1992}, pages={129–142} }
@inproceedings{brown_york_1992, title={Temperature and time in the geometry of rotating black holes}, url={http://inspirehep.net/record/332517}, booktitle={NATO Workshop on the Physical Origin of Time Asymmetry}, author={Brown, J.David and York, James W., Jr.}, year={1992}, month={Jan} }
@article{brown_martinez_york_1991, title={COMPLEX KERR-NEWMAN GEOMETRY AND BLACK-HOLE THERMODYNAMICS}, volume={66}, ISSN={["0031-9007"]}, url={http://inspirehep.net/record/300355}, DOI={10.1103/PhysRevLett.66.2281}, abstractNote={We establish that in the functional-integral expression for the grand partition function, the thermodynamic properties of a charged, rotating black hole are derived from a complex geometry. The corresponding real ``thermodynamical'' action is constructed explicitly.}, number={18}, journal={PHYSICAL REVIEW LETTERS}, author={BROWN, JD and MARTINEZ, EA and YORK, JW}, year={1991}, month={May}, pages={2281–2284} }
@inproceedings{brown_york_1991, title={Quasilocal energy in general relativity}, url={http://inspirehep.net/record/322580}, booktitle={Joint Summer Reasearch Conference on Mathematical Aspects of Classical Field Theory}, author={Brown, J.David and York, James W., Jr.}, year={1991}, month={Jul} }
@inproceedings{brown_martinez_york_1991, title={Rotating black holes, complex geometry, and thermodynamics}, volume={631}, url={http://inspirehep.net/record/299892}, DOI={10.1111/j.1749-6632.1991.tb52645.x}, abstractNote={Annals of the New York Academy of SciencesVolume 631, Issue 1 p. 225-234 Rotating Black Holes, Complex Geometry, and Thermodynamicsa, b J. DAVID BROWN, J. DAVID BROWN Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255Search for more papers by this authorERIK A. MARTINEZ, ERIK A. MARTINEZ Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255Search for more papers by this authorJAMES W. YORK JR, JAMES W. YORK JR Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255Search for more papers by this author J. DAVID BROWN, J. DAVID BROWN Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255Search for more papers by this authorERIK A. MARTINEZ, ERIK A. MARTINEZ Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255Search for more papers by this authorJAMES W. YORK JR, JAMES W. YORK JR Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255Search for more papers by this author First published: August 1991 https://doi.org/10.1111/j.1749-6632.1991.tb52645.xCitations: 11 a Research support was received from National Science Foundation Grants PHY-8407492 and PHY-8908741. b Revised version: December 1990. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume631, Issue1Nonlinear Problems in Relativity and CosmologyAugust 1991Pages 225-234 RelatedInformation}, booktitle={Annals of the New York Academy of Sciences}, author={Brown, J. D. and Martinez, E. A. and York, J. W.}, year={1991}, pages={225–234} }
@article{braden_brown_whiting_york_1990, title={CHARGED BLACK-HOLE IN A GRAND CANONICAL ENSEMBLE}, volume={42}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/297575}, DOI={10.1103/physrevd.42.3376}, abstractNote={A spherical charged black hole in thermal equilibrium is considered from the perspective of a grand canonical ensemble in which the electrostatic potential, temperature, and surface area are specified at a finite boundary. A correspondence is established between the boundary-value data of a well-posed problem in a finite region of Euclidean spacetime and the freely chosen thermodynamic data specifying the ensemble. The Hamiltonian and Gauss's-law constraints are solved and eliminated from the Einstein-Maxwell action, producing a "reduced action" that depends upon two remaining degrees of freedom (two free parameters), as well as on the thermodynamic data. The black-hole temperature, entropy, and corresponding electrostatic potential then follow from relations holding at the stationary points of the reduced action with respect to variation of the free parameters. Investigation of an appropriate eigenvalue problem shows that the criteria for local dynamical and thermodynamical stability are the same. The ensemble can be either stable or unstable, depending upon a certain relation involving mean charge, gravitational radius, and boundary radius. The role of the reduced action in determining the grand partition function, the thermodynamics of charged black holes, and the density of states is discussed.}, number={10}, journal={PHYSICAL REVIEW D}, author={BRADEN, HW and BROWN, JD and WHITING, BF and YORK, JW}, year={1990}, month={Nov}, pages={3376–3385} }
@article{brown_martinez_1990, title={LORENTZIAN PATH INTEGRAL FOR MINISUPERSPACE COSMOLOGY}, volume={42}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/296280}, DOI={10.1103/physrevd.42.1931}, abstractNote={The path integral for minisuperspace models of cosmology is defined as a sum over Lorentzian geometries, and is a Green function for the Wheeler-DeWitt operator. It is shown to be a symmetric function of the initial and final configurations, and its real part is a solution to the Wheeler-DeWitt equation. The Lorentzian path integral is computed explicitly for the de Sitter minisuper-space model and is convergent. The resulting Green function is then related to the solutions of the Wheeler-DeWitt equation known as the Hartle-Hawking and tunneling wave functions of the Universe. The real part of this Green function is a product of Hartle-Hawking wave functions.}, number={6}, journal={PHYSICAL REVIEW D}, author={BROWN, JD and MARTINEZ, EA}, year={1990}, month={Sep}, pages={1931–1943} }
@article{brown_comer_martinez_melmed_whiting_york_1990, title={THERMODYNAMIC ENSEMBLES AND GRAVITATION}, volume={7}, ISSN={["0264-9381"]}, url={http://inspirehep.net/record/279180}, DOI={10.1088/0264-9381/7/8/020}, abstractNote={By including gravitation as described by general relativity as a part of a thermodynamic system, the authors have obtained formal path integral representations of partition functions for various ensembles including that appropriate to the microcanonical ensemble. This is possible because the boundary conditions for certain well posed Euclidean problems in general relativity exactly correspond to boundary conditions of certain well posed problems in thermodynamics. The different ensembles are obtained using the definition of variables conjugate both in the sense of the field theory of general relativity and in the sense of thermodynamics, the boundary data of which can be prescribed geometrically using gravity.}, number={8}, journal={CLASSICAL AND QUANTUM GRAVITY}, author={BROWN, JD and COMER, GL and MARTINEZ, EA and MELMED, J and WHITING, BF and YORK, JW}, year={1990}, month={Aug}, pages={1433–1444} }
@article{brown_1990, title={TUNNELING IN PERFECT-FLUID (MINISUPERSPACE) QUANTUM COSMOLOGY}, volume={41}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/282512}, DOI={10.1103/physrevd.41.1125}, number={4}, journal={PHYSICAL REVIEW D}, author={BROWN, JD}, year={1990}, month={Feb}, pages={1125–1141} }
@article{brown_york_1989, title={JACOBI ACTION AND THE RECOVERY OF TIME IN GENERAL-RELATIVITY}, volume={40}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/287903}, DOI={10.1103/physrevd.40.3312}, abstractNote={We argue that the usual action principle of general relativity, applied to spacetimes with closed spatial geometries, should be regarded as analogous to Jacobi's form of the principle of stationary action, in which the energy rather than a physical time is fixed. Following the paradigm of quantization based on Jacobi's action for a nonrelativistic particle, we show that the Wheeler-DeWitt equation corresponds to a time-independent Schr\odinger equation. The relationship between Jacobi's and Hamilton's action principles then allows us to derive a time-dependent Wheeler-DeWitt equation of the Schr\odinger type. In this equation, the role of energy is played by the cosmological constant and that of physical time by the four-volume of spacetime.}, number={10}, journal={PHYSICAL REVIEW D}, author={BROWN, JD and YORK, JW}, year={1989}, month={Nov}, pages={3312–3318} }
@article{brown_burgess_kshirsagar_whiting_york_1989, title={SCALAR FIELD WORMHOLES}, volume={328}, ISSN={["0550-3213"]}, DOI={10.1016/0550-3213(89)90101-6}, abstractNote={Abstract A classical wormhole solution is constructed for gravity couples to a positive energg, maplese scalar field. We examine carefully the definitions of euclideanization, and find that this solution is equivalent to the wormhole previously obtained for gravity coupled to an antisymmetric, two-index gauge potential, which is locally dual to the scalar field. However, as we explain, this wormhole solution is characterized by a scalar field configuration which is co.}, number={1}, journal={NUCLEAR PHYSICS B}, author={BROWN, JD and BURGESS, CP and KSHIRSAGAR, A and WHITING, BF and YORK, JW}, year={1989}, month={Dec}, pages={213–222} }
@book{brown_1988, title={Lower dimensional gravity}, ISBN={997150622X}, url={http://inspirehep.net/record/269097}, DOI={10.1142/0622}, abstractNote={This book addresses the subject of gravity theories in two and three spacetime dimensions. The prevailing philosophy is that lower dimensional models of gravity provide a useful arena for developing new ideas and insights, which are applicable to four dimensional gravity. The first chapter consists of a comprehensive introduction to both two and three dimensional gravity, including a discussion of their basic structures. In the second chapter, the asymptotic structure of three dimensional Einstein gravity with a negative cosmological constant is analyzed. The third chapter contains a treatment of the effects of matter sources in classical two dimensional gravity. The fourth chapter gives a complete analysis of particle pair creation by electric and gravitational fields in two dimensions, and the resulting effect on the cosmological constant. Lower dimensional gravity may have never been reviewed in its entirety anywhere in the literature.}, publisher={Singapore: World Scientific}, author={Brown, J. D.}, year={1988} }
@article{brown_teitelboim_1988, title={NEUTRALIZATION OF THE COSMOLOGICAL CONSTANT BY MEMBRANE CREATION}, volume={297}, ISSN={["0550-3213"]}, url={http://inspirehep.net/record/264194}, DOI={10.1016/0550-3213(88)90559-7}, abstractNote={The quantum creation of closed membranes by totally antisymmetric tensor and gravitational fields is considered in arbitrary space-time dimension. The creation event is described by instanton tunneling. As membranes are produced, the energy density associated with the antisymmetric tensor fielld decreases, reducing the effective value of the cosmological constant. For a wide range of parameters and initial conditions, this process will naturally stop as soon as the cosmological constant is near zero, even if the energy remaining in the antisymmetric tensor field is large. Among the instantons obtained, some are interpreted as representing a topology change, in which an open space spontaneously compactifies; however, the quantum probability for these processes vanishes.}, number={4}, journal={NUCLEAR PHYSICS B}, author={BROWN, JD and TEITELBOIM, C}, year={1988}, month={Feb}, pages={787–836} }
@article{brown_teitelboim_1987, title={DYNAMIC NEUTRALIZATION OF THE COSMOLOGICAL CONSTANT}, volume={195}, ISSN={["0370-2693"]}, url={http://inspirehep.net/record/254076}, DOI={10.1016/0370-2693(87)91190-7}, abstractNote={A dynamical process is described in which the cosmological constant is netralized through the quantum creation of closed membranes by totally antisymmetric tensor and gravitational fields.}, number={2}, journal={PHYSICS LETTERS B}, author={BROWN, JD and TEITELBOIM, C}, year={1987}, month={Sep}, pages={177–182} }
@article{brown_henneaux_teitelboim_1986, title={BLACK-HOLES IN 2 SPACETIME DIMENSIONS}, volume={33}, ISSN={["0556-2821"]}, url={http://inspirehep.net/record/228728}, DOI={10.1103/PhysRevD.33.319}, abstractNote={It is shown that the analog of the black hole exists in two-dimensional gravity. It is given by a metric which solves the vacuum field equation (constant curvature) everywhere except on a singular line. This geometry possesses an event horizon. There is as well an analog of Hawking radiation with temperature proportional to the strength (mass) of the singularity.}, number={2}, journal={PHYSICAL REVIEW D}, author={BROWN, JD and HENNEAUX, M and TEITELBOIM, C}, year={1986}, month={Jan}, pages={319–323} }
@article{brown_henneaux_1986, title={CENTRAL CHARGES IN THE CANONICAL REALIZATION OF ASYMPTOTIC SYMMETRIES - AN EXAMPLE FROM 3-DIMENSIONAL GRAVITY}, volume={104}, ISSN={["0010-3616"]}, url={http://inspirehep.net/record/231928}, DOI={10.1007/BF01211590}, abstractNote={It is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level. This is done by studying three dimensional gravity with a negative cosmological constant. The asymptotic symmetry group in that case is eitherR×SO(2) or the pseudo-conformal group in two dimensions, depending on the boundary conditions adopted at spatial infinity. In the latter situation, a nontrivial central charge appears in the algebra of the canonical generators, which turns out to be just the Virasoro central charge.}, number={2}, journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS}, author={BROWN, JD and HENNEAUX, M}, year={1986}, pages={207–226} }
@article{brown_henneaux_1986, title={ON THE POISSON BRACKETS OF DIFFERENTIABLE GENERATORS IN CLASSICAL FIELD-THEORY}, volume={27}, ISSN={["0022-2488"]}, url={http://inspirehep.net/record/229338}, DOI={10.1063/1.527249}, abstractNote={The canonical formulation of field theory on open spaces is considered. It is proved, under appropriate assumptions, that the Poisson bracket of two differentiable generators is also a differentiable generator.}, number={2}, journal={JOURNAL OF MATHEMATICAL PHYSICS}, author={BROWN, JD and HENNEAUX, M}, year={1986}, month={Feb}, pages={489–491} }
@article{mikaelian_samuel_brown_1980, title={LOWEST ORDER G-2 OF W+/- BOSONS}, volume={27}, ISSN={["0024-1318"]}, url={http://inspirehep.net/record/141600}, DOI={10.1007/bf02817160}, number={7}, journal={LETTERE AL NUOVO CIMENTO}, author={MIKAELIAN, KO and SAMUEL, MA and BROWN, D}, year={1980}, pages={211–214} }
@article{sibley_martin_wintersgill_brown_1979, title={EFFECT OF RADIATION ON THE OH- INFRARED-ABSORPTION OF QUARTZ CRYSTALS}, volume={50}, ISSN={["0021-8979"]}, DOI={10.1063/1.326596}, abstractNote={The effect of 1.6‐MeV‐electron irradiation on the infrared properties of high‐purity quartz crystals has been studied. The infrared bands assciated with OH− impurities in SiO2 crystals are strongly temperature dependent and must be studied at 77 K or below. Prolonged electron irradiation at low temperature suppresses all of the OH− bands, but these bands recover when the crystals are annealed to approximately 740 K. If as‐grown crystals are irradiated at 300 K, the intensity of the OH− bands decreases and two new bands appear at 3367 and 3306 cm−1. The relative absorption intensity of these two bands depends on radiation temperature and dose.}, number={8}, journal={JOURNAL OF APPLIED PHYSICS}, author={SIBLEY, WA and MARTIN, JJ and WINTERSGILL, MC and BROWN, JD}, year={1979}, pages={5449–5452} }