The minus sign in the first law of de Sitter horizons. (English) Zbl 1540.83035
Summary: Due to a well-known, but curious, minus sign in the Gibbons-Hawking first law for the static patch of de Sitter space, the entropy of the cosmological horizon is reduced by the addition of Killing energy. This minus sign raises the puzzling question how the thermodynamics of the static patch should be understood. We argue the confusion arises because of a mistaken interpretation of the matter Killing energy as the total internal energy, and resolve the puzzle by introducing a system boundary at which a proper thermodynamic ensemble can be specified. When this boundary shrinks to zero size the total internal energy of the ensemble (the Brown-York energy) vanishes, as does its variation. Part of this vanishing variation is thermalized, captured by the horizon entropy variation, and part is the matter contribution, which may or may not be thermalized. If the matter is in global equilibrium at the de Sitter temperature, the first law becomes the statement that the generalized entropy is stationary.
MSC:
| 83C57 | Black holes |
| 83C45 | Quantization of the gravitational field |
| 81P17 | Quantum entropies |
| 80A10 | Classical and relativistic thermodynamics |
References:
| [1] | J.D. Bekenstein, Black holes and entropy, Phys. Rev. D7 (1973) 2333 [INSPIRE]. · Zbl 1369.83037 |
| [2] | J.M. Bardeen, B. Carter and S.W. Hawking, The four laws of black hole mechanics, Commun. Math. Phys.31 (1973) 161 [INSPIRE]. · Zbl 1125.83309 |
| [3] | S.W. Hawking, Particle creation by black holes, Commun. Math. Phys.43 (1975) 199 [INSPIRE]. · Zbl 1378.83040 |
| [4] | G.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D15 (1977) 2752 [INSPIRE]. |
| [5] | Dolan, BP; Kastor, D.; Kubiznak, D.; Mann, RB; Traschen, J., Thermodynamic volumes and isoperimetric inequalities for de Sitter black holes, Phys. Rev. D, 87 (2013) · doi:10.1103/PhysRevD.87.104017 |
| [6] | R.D. Sorkin, The statistical mechanics of black hole thermodynamics, in Symposium on black holes and relativistic stars (dedicated to memory of S. Chandrasekhar), (1997) [gr-qc/9705006] [INSPIRE]. · Zbl 0946.83034 |
| [7] | M. Spradlin, A. Strominger and A. Volovich, Les Houches lectures on de Sitter space, in Les Houches summer school: session 76. Euro summer school on unity of fundamental physics: gravity, gauge theory and strings, (2001), p. 423 [hep-th/0110007] [INSPIRE]. |
| [8] | Dinsmore, J.; Draper, P.; Kastor, D.; Qiu, Y.; Traschen, J., Schottky anomaly of de Sitter black holes, Class. Quant. Grav., 37 (2020) · Zbl 1478.83145 · doi:10.1088/1361-6382/ab638f |
| [9] | Anninos, D., De Sitter musings, Int. J. Mod. Phys. A, 27, 1230013 (2012) · Zbl 1247.83068 · doi:10.1142/S0217751X1230013X |
| [10] | Klemm, D.; Vanzo, L., Aspects of quantum gravity in de Sitter spaces, JCAP, 11, 006 (2004) · doi:10.1088/1475-7516/2004/11/006 |
| [11] | Banks, T., Cosmological breaking of supersymmetry?, Int. J. Mod. Phys. A, 16, 910 (2001) · Zbl 0982.83040 · doi:10.1142/S0217751X01003998 |
| [12] | W. Fischler, Taking de Sitter seriously, talk given at Role of scaling laws in physics and biology (celebrating the 60^thbirthday of Geoffrey West), Santa Fe, NM, U.S.A. (2000). |
| [13] | Jacobson, T.; Visser, M., Gravitational thermodynamics of causal diamonds in (A)dS, SciPost Phys., 7, 079 (2019) · doi:10.21468/SciPostPhys.7.6.079 |
| [14] | Jacobson, T.; Visser, M., Spacetime equilibrium at negative temperature and the attraction of gravity, Int. J. Mod. Phys. D, 28, 1944016 (2019) · doi:10.1142/S0218271819440164 |
| [15] | Banks, T.; Fiol, B.; Morisse, A., Towards a quantum theory of de Sitter space, JHEP, 12, 004 (2006) · Zbl 1226.83021 · doi:10.1088/1126-6708/2006/12/004 |
| [16] | T. Banks and W. Fischler, Holographic theory of accelerated observers, the S-matrix, and the emergence of effective field theory, arXiv:1301.5924 [INSPIRE]. |
| [17] | T. Banks and W. Fischler, Why the cosmological constant is a boundary condition, arXiv:1811.00130 [INSPIRE]. |
| [18] | T. Banks and W. Fischler, Holographic cosmology 3.0, Phys. Scripta T117 (2005) 56 [hep-th/0310288] [INSPIRE]. |
| [19] | Dong, X.; Silverstein, E.; Torroba, G., De Sitter holography and entanglement entropy, JHEP, 07, 050 (2018) · Zbl 1395.81213 · doi:10.1007/JHEP07(2018)050 |
| [20] | Banihashemi, B.; Jacobson, T., Thermodynamic ensembles with cosmological horizons, JHEP, 07, 042 (2022) · Zbl 1522.83125 · doi:10.1007/JHEP07(2022)042 |
| [21] | V. Chandrasekaran, R. Longo, G. Penington and E. Witten, An algebra of observables for de Sitter space, arXiv:2206.10780 [INSPIRE]. |
| [22] | J.W. York, Jr., Black hole thermodynamics and the Euclidean Einstein action, Phys. Rev. D33 (1986) 2092 [INSPIRE]. · Zbl 1058.83514 |
| [23] | B.F. Whiting and J.W. York, Jr., Action principle and partition function for the gravitational field in black hole topologies, Phys. Rev. Lett.61 (1988) 1336 [INSPIRE]. |
| [24] | H.W. Braden, J.D. Brown, B.F. Whiting and J.W. York, Jr., Charged black hole in a grand canonical ensemble, Phys. Rev. D42 (1990) 3376 [INSPIRE]. |
| [25] | Brown, JD; York, JW Jr, Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D, 47, 1407 (1993) · doi:10.1103/PhysRevD.47.1407 |
| [26] | Brown, JD; York, JW Jr, The microcanonical functional integral. 1. The gravitational field, Phys. Rev. D, 47, 1420 (1993) · doi:10.1103/PhysRevD.47.1420 |
| [27] | Brown, JD; Creighton, J.; Mann, RB, Temperature, energy and heat capacity of asymptotically anti-de Sitter black holes, Phys. Rev. D, 50, 6394 (1994) · doi:10.1103/PhysRevD.50.6394 |
| [28] | G. Hayward, Euclidean action and the thermodynamics of manifolds without boundary, Phys. Rev. D41 (1990) 3248 [INSPIRE]. |
| [29] | Miyashita, S., Gravitational and gravitoscalar thermodynamics, JHEP, 09, 121 (2021) · Zbl 1472.83042 · doi:10.1007/JHEP09(2021)121 |
| [30] | Svesko, A.; Verheijden, E.; Verlinde, EP; Visser, MR, Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity, JHEP, 08, 075 (2022) · Zbl 1522.83242 · doi:10.1007/JHEP08(2022)075 |
| [31] | Draper, P.; Farkas, S., Euclidean de Sitter black holes and microcanonical equilibrium, Phys. Rev. D, 105 (2022) · doi:10.1103/PhysRevD.105.126021 |
| [32] | Martinez, EA, The postulates of gravitational thermodynamics, Phys. Rev. D, 54, 6302 (1996) · doi:10.1103/PhysRevD.54.6302 |
| [33] | E. Coleman et al., De Sitter microstates from \(T\overline{T} \) + Λ_2and the Hawking-Page transition, JHEP07 (2022) 140 [arXiv:2110.14670] [INSPIRE]. · Zbl 1522.83151 |
| [34] | Z. An and M.T. Anderson, The initial boundary value problem and quasi-local Hamiltonians in general relativity, arXiv:2103.15673 [INSPIRE]. |
| [35] | Andrade, T.; Kelly, WR; Marolf, D.; Santos, JE, On the stability of gravity with Dirichlet walls, Class. Quant. Grav., 32 (2015) · Zbl 1329.83038 · doi:10.1088/0264-9381/32/23/235006 |
| [36] | Iyer, V., Lagrangian perfect fluids and black hole mechanics, Phys. Rev. D, 55, 3411 (1997) · doi:10.1103/PhysRevD.55.3411 |
| [37] | Blanco, DD; Casini, H.; Hung, L-Y; Myers, RC, Relative entropy and holography, JHEP, 08, 060 (2013) · Zbl 1342.83128 · doi:10.1007/JHEP08(2013)060 |
| [38] | Pedraza, JF; Svesko, A.; Sybesma, W.; Visser, MR, Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity, JHEP, 12, 134 (2021) · Zbl 1521.83145 · doi:10.1007/JHEP12(2021)134 |
| [39] | S.W. Hawking and J.B. Hartle, Energy and angular momentum flow into a black hole, Commun. Math. Phys.27 (1972) 283 [INSPIRE]. |
| [40] | B. Carter, The general theory of the mechanical, electromagnetic and thermodynamic properties of black holes, in General relativity: an Einstein centenary survey, S.W. Hawking and W. Israel eds., Cambridge University Press (1979), p. 294. |
| [41] | R.M. Wald, Quantum field theory in curved space-time and black hole thermodynamics, University of Chicago Press, Chicago, IL, U.S.A. (1995) [INSPIRE]. |
| [42] | Jacobson, T.; Parentani, R., Horizon entropy, Found. Phys., 33, 323 (2003) · doi:10.1023/A:1023785123428 |
| [43] | Amsel, AJ; Marolf, D.; Virmani, A., The physical process first law for bifurcate Killing horizons, Phys. Rev. D, 77 (2008) · doi:10.1103/PhysRevD.77.024011 |
| [44] | Emparan, R.; Pedraza, JF; Svesko, A.; Tomašević, M.; Visser, MR, Black holes in dS_3, JHEP, 11, 073 (2022) · Zbl 1536.83058 · doi:10.1007/JHEP11(2022)073 |
| [45] | S. Deser and R. Jackiw, Three-dimensional cosmological gravity: dynamics of constant curvature, Annals Phys.153 (1984) 405 [INSPIRE]. |
| [46] | Klemm, D.; Vanzo, L., De Sitter gravity and Liouville theory, JHEP, 04, 030 (2002) · doi:10.1088/1126-6708/2002/04/030 |
| [47] | Balasubramanian, V.; de Boer, J.; Minic, D., Mass, entropy and holography in asymptotically de Sitter spaces, Phys. Rev. D, 65 (2002) · doi:10.1103/PhysRevD.65.123508 |
| [48] | Parikh, M.; Wilczek, F., An action for black hole membranes, Phys. Rev. D, 58 (1998) · doi:10.1103/PhysRevD.58.064011 |
| [49] | L. Susskind, Black holes hint towards de Sitter-matrix theory, arXiv:2109.01322 [INSPIRE]. |
| [50] | Susskind, L., Entanglement and chaos in de Sitter space holography: an SYK example, JHAP, 1, 1 (2021) |
| [51] | Shaghoulian, E., The central dogma and cosmological horizons, JHEP, 01, 132 (2022) · Zbl 1521.83148 · doi:10.1007/JHEP01(2022)132 |
| [52] | Anninos, D.; Hartnoll, SA; Hofman, DM, Static patch solipsism: conformal symmetry of the de Sitter worldline, Class. Quant. Grav., 29 (2012) · Zbl 1253.83014 · doi:10.1088/0264-9381/29/7/075002 |
| [53] | Anninos, D.; Hofman, DM, Infrared realization of dS_2in AdS_2, Class. Quant. Grav., 35 (2018) · Zbl 1409.83135 · doi:10.1088/1361-6382/aab143 |
| [54] | Leuven, S.; Verlinde, E.; Visser, M., Towards non-AdS holography via the long string phenomenon, JHEP, 06, 097 (2018) · Zbl 1395.81250 · doi:10.1007/JHEP06(2018)097 |
| [55] | R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D48 (1993) R3427 [gr-qc/9307038] [INSPIRE]. · Zbl 0942.83512 |
| [56] | Iyer, V.; Wald, RM, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D, 50, 846 (1994) · doi:10.1103/PhysRevD.50.846 |
| [57] | Iyer, V.; Wald, RM, A comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes, Phys. Rev. D, 52, 4430 (1995) · doi:10.1103/PhysRevD.52.4430 |
| [58] | Harlow, D.; Wu, J-Q, Covariant phase space with boundaries, JHEP, 10, 146 (2020) · Zbl 1461.83007 · doi:10.1007/JHEP10(2020)146 |
| [59] | Chao, W-Z, Quantum creation of a black hole, Int. J. Mod. Phys. D, 6, 199 (1997) · Zbl 0936.83034 · doi:10.1142/S0218271897000121 |
| [60] | Bousso, R.; Hawking, SW, Lorentzian condition in quantum gravity, Phys. Rev. D, 59 (1999) · doi:10.1103/PhysRevD.59.103501 |
| [61] | Gregory, R.; Moss, IG; Withers, B., Black holes as bubble nucleation sites, JHEP, 03, 081 (2014) · Zbl 1333.83084 · doi:10.1007/JHEP03(2014)081 |
| [62] | Draper, P.; Farkas, S., De Sitter black holes as constrained states in the Euclidean path integral, Phys. Rev. D, 105 (2022) · doi:10.1103/PhysRevD.105.126022 |
| [63] | E.K. Morvan, J.P. van der Schaar and M.R. Visser, On the Euclidean action of de Sitter black holes and constrained instantons, arXiv:2203.06155 [INSPIRE]. |
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