@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 definitionE 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 light cone Np belonging to a generic spacetime point p .A s a power series in r, we compute the energy E of the gravitational and matter fields on a spacelike hypersurface S 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 ‘‘light cone reference,’’ which stems from a certain isometric embedding of S(r) into a genuine light cone of Minkowski spacetime. Choosing this zero point, we find the following results: ~i! in the presence of matter E5 4 3 pr 3 @T mnu m u n #u p1O(r 4 ) and ~ii! in vacuo E5 1 90 r 5 @T mnlku m u n u l u k #u p1O(r 6 ). Here, u m is a unit, future-pointing, timelike vector in the tangent space at p ~which defines the choice of affine radius !; Tmn is the matter stress-energy-momentum tensor; Tmnlk is the Bel-Robinson gravitational super stress-energymomentum tensor; and u p denotes ‘‘restriction to p.’’ Hawking’s quasilocal mass expression agrees with the results ~i! and ~ii! up to and including the first non-trivial order in the affine radius. The non-vacuum result~i! has the expected form based on the results of Newtonian potential theory. @S0556-2821~99!02904-5#}, number={6}, journal={PHYSICAL REVIEW D}, author={Brown, JD and Lau, SR and York, JW}, year={1999}, month={Mar} }
 @article{york_1999, title={Conformal "thin-sandwich" data for the initial-value problem of general relativity}, volume={82}, ISSN={["0031-9007"]}, DOI={10.1103/PhysRevLett.82.1350}, abstractNote={The initial-value problem is posed by giving a conformal three-metric on each of two nearby spacelike hypersurfaces, their proper-time separation up to a multiplier to be determined, and the mean (extrinsic) curvature of one slice. The resulting equations have the same elliptic form as does the one-hypersurface formulation. The metrical roots of this form are revealed by a conformal “thin sandwich” viewpoint coupled with the transformation prop-erties of the lapse function.}, number={7}, journal={PHYSICAL REVIEW LETTERS}, author={York, JW}, year={1999}, month={Feb}, pages={1350–1353} }
 @book{davis_chu_mcconnell_dolan_norris_ortiz_plemmon_ridgeway_scaife_stewart_et al._1998, title={Cornelius Lanczos: Collected published papers with commentaries}, ISBN={0929493003}, publisher={Raleigh, NC: College of Physical and Mathematical Sciences, North Carolina State University}, author={Davis, W. R. and Chu, M. T. and McConnell, J. R. and Dolan, P. and Norris, L. K. and Ortiz, E. and Plemmon, R. J. and Ridgeway, D. and Scaife, B.K.P. and Stewart, W. J. and et al.}, year={1998} }
 @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 S contained within a finite topologically spherical boundary B5]S. 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. @S0556-2821~97!03104-4#}, number={4}, journal={PHYSICAL REVIEW D}, author={Brown, JD and Lau, SR and York, JW}, year={1997}, month={Feb}, pages={1977–1984} }
 @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 [ital 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 [sup 3][ital 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 [sup 3][ital B]. The integral of the energy surface density over such a two-surface [ital B] is the quasilocal energy associated with a spacelike three-surface [Sigma] whose orthogonal intersection with [sup 3][ital B] is the boundary [ital B]. The resulting expression for quasilocal energy is given in terms of the total mean curvature of the spatial boundary [ital B] as a surface embedded in [Sigma]. The quasilocal energy is also the value of the Hamiltonian that generates unit magnitude proper-time translations on [sup 3][ital B] in the timelike direction orthogonal to [ital B]. Conserved charges such as angular momentum are defined using the surface stress tensor and Killing vector fields on [sup 3][ital B]. For spacetimes that are asymptoticallymore » 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.« less}, 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} }
 @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_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_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_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={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} }