×

Conserved charges in asymptotically de Sitter spacetimes. (English) Zbl 1478.83046

Summary: We present a covariant phase space construction of hamiltonian generators of asymptotic symmetries with ‘Dirichlet’ boundary conditions in de Sitter spacetime, extending a previous study of Jäger. We show that the de Sitter charges so defined are identical to those of Ashtekar, Bonga, and Kesavan (ABK). We then present a comparison of ABK charges with other notions of de Sitter charges. We compare ABK charges with counterterm charges, showing that they differ only by a constant offset, which is determined in terms of the boundary metric alone. We also compare ABK charges with charges defined by Kelly and Marolf at spatial infinity of de sitter spacetime. When the formalisms can be compared, we show that the two definitions agree. Finally, we express Kerr-de Sitter metrics in four and five dimensions in an appropriate Fefferman-Graham form.

MSC:

83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
83C15 Exact solutions to problems in general relativity and gravitational theory
83C40 Gravitational energy and conservation laws; groups of motions
35G15 Boundary value problems for linear higher-order PDEs
58J32 Boundary value problems on manifolds
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Abbott L F and Deser S 1982 Stability of gravity with a cosmological constant Nucl. Phys. B 195 76 · Zbl 0900.53033 · doi:10.1016/0550-3213(82)90049-9
[2] Strominger A 2001 The dS / CFT correspondence J. High Energy Phys.JHEP10(2001) 034 · doi:10.1088/1126-6708/2001/10/034
[3] Balasubramanian V, de Boer J and Minic D 2002 Mass, entropy and holography in asymptotically de Sitter spaces Phys. Rev. D 65 123508 · doi:10.1103/PhysRevD.65.123508
[4] Kastor D and Traschen J H 2002 A positive energy theorem for asymptotically de Sitter space-times Class. Quantum Grav.19 5901 · Zbl 1019.83007 · doi:10.1088/0264-9381/19/23/302
[5] Jäger S 2008 Conserved quantities in asymptotically de Sitter spacetimes (Göttingen, Germany: The University of Göttingen) Master’s Thesis
[6] Anninos D, Ng G S and Strominger A 2011 Asymptotic symmetries and charges in De Sitter space Class. Quantum Grav.28 175019 · Zbl 1225.83019 · doi:10.1088/0264-9381/28/17/175019
[7] Kelly W R and Marolf D 2012 Phase spaces for asymptotically de Sitter cosmologies Class. Quantum Grav.29 205013 · Zbl 1256.83034 · doi:10.1088/0264-9381/29/20/205013
[8] Ashtekar A, Bonga B and Kesavan A 2015 Asymptotics with a positive cosmological constant: I. Basic framework Class. Quantum Grav.32 025004 · Zbl 1307.83011 · doi:10.1088/0264-9381/32/2/025004
[9] Poole A, Skenderis K and Taylor M 2018 (A)dS4 in bondi gauge Class. Quantum Grav.36 095005 · Zbl 1476.83031 · doi:10.1088/1361-6382/ab117c
[10] Anninos D 2012 De Sitter musings Int. J. Mod. Phys. A 27 1230013 · Zbl 1247.83068 · doi:10.1142/S0217751X1230013X
[11] Ashtekar A 2017 Implications of a positive cosmological constant for general relativity Rep. Prog. Phys.80 102901 · doi:10.1088/1361-6633/aa7bb1
[12] Szabados L B and Tod P 2018 A review of total energy-momenta in GR with a positive cosmological constant Int. J. Mod. Phys.28 1930003 · doi:10.1142/S0218271819300039
[13] Ashtekar A, Bonga B and Kesavan A 2015 Asymptotics with a positive cosmological constant. II. Linear fields on de Sitter spacetime Phys. Rev. D 92 044011 · doi:10.1103/PhysRevD.92.044011
[14] Ashtekar A, Bonga B and Kesavan A 2015 Asymptotics with a positive cosmological constant: III. The quadrupole formula Phys. Rev. D 92 104032 · doi:10.1103/PhysRevD.92.104032
[15] Ashtekar A, Bonga B and Kesavan A 2016 Gravitational waves from isolated systems: surprising consequences of a positive cosmological constant Phys. Rev. Lett.116 051101 · Zbl 1356.83005 · doi:10.1103/PhysRevLett.116.051101
[16] Date G and Hoque S J 2016 Gravitational waves from compact sources in a de Sitter background Phys. Rev. D 94 064039 · doi:10.1103/PhysRevD.94.064039
[17] Date G and Hoque S J 2017 Cosmological horizon and the quadrupole formula in de Sitter background Phys. Rev. D 96 044026 · doi:10.1103/PhysRevD.96.044026
[18] Hoque S J and Virmani A 2018 On propagation of energy flux in de Sitter spacetime Gen. Relativ. Gravit.50 40 · Zbl 1392.83025 · doi:10.1007/s10714-018-2359-3
[19] Wald R M and Zoupas A 2000 A general definition of ‘conserved quantities’ in general relativity and other theories of gravity Phys. Rev. D 61 084027 · Zbl 1136.83317 · doi:10.1103/PhysRevD.61.084027
[20] Hollands S, Ishibashi A and Marolf D 2005 Comparison between various notions of conserved charges in asymptotically AdS-spacetimes Class. Quantum Grav.22 2881 · Zbl 1082.83014 · doi:10.1088/0264-9381/22/14/004
[21] Klemm D 2002 Some aspects of the de Sitter / CFT correspondence Nucl. Phys. B 625 295 · Zbl 0985.81115 · doi:10.1016/S0550-3213(02)00007-X
[22] Nojiri S and Odintsov S D 2001 Conformal anomaly from dS / CFT correspondence Phys. Lett. B 519 145 · Zbl 0972.81169 · doi:10.1016/S0370-2693(01)00869-3
[23] Wald R M 1984 General Relativity (Chicago, IL: University of Chicago Press) (https://doi.org/10.7208/chicago/9780226870373.001.0001) · Zbl 0549.53001 · doi:10.7208/chicago/9780226870373.001.0001
[24] Ashtekar A, Bombelli L and Reula O 1991 The covariant phase space of asymptotically flat gravitational fields Analysis, Geometry and Mechanics: 200 Years After Lagrange ed M Francaviglia and D Holm (Amsterdam: North-Holland) · Zbl 0717.53056 · doi:10.1016/B978-0-444-88958-4.50021-5
[25] Lee J and Wald R M 1990 Local symmetries and constraints J. Math. Phys.31 725 · Zbl 0704.70013 · doi:10.1063/1.528801
[26] Iyer V and Wald R M 1994 Some properties of noether charge and a proposal for dynamical black hole entropy Phys. Rev. D 50 846 · doi:10.1103/PhysRevD.50.846
[27] Compère G and Fiorucci A 2019 Advanced Lectures in General Relativity(Lecture Notes in Physics vol 952) (Berlin: Springer) pp 14-32 · Zbl 1419.83003 · doi:10.1007/978-3-030-04260-8
[28] Wald R M 1990 On identically closed forms locally constructed from a field J. Math. Phys.31 2378-84 · Zbl 0728.53064 · doi:10.1063/1.528839
[29] Balasubramanian V and Kraus P 1999 A stress tensor for Anti-de Sitter gravity Commun. Math. Phys.208 413 · Zbl 0946.83013 · doi:10.1007/s002200050764
[30] Emparan R, Johnson C V and Myers R C 1999 Surface terms as counterterms in the AdS / CFT correspondence Phys. Rev. D 60 104001 · doi:10.1103/PhysRevD.60.104001
[31] de Boer J, Verlinde E P and Verlinde H L 2000 On the holographic renormalization group J. High Energ. Phys.JHEP08(2000) 003 · Zbl 0989.81538 · doi:10.1088/1126-6708/2000/08/003
[32] de Haro S, Solodukhin S N and Skenderis K 2001 Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence Commun. Math. Phys.217 595-622 · Zbl 0984.83043 · doi:10.1007/s002200100381
[33] Papadimitriou I and Skenderis K 2005 Thermodynamics of asymptotically locally AdS spacetimes J. High Energy Phys.JHEP08(2005) 004 · doi:10.1088/1126-6708/2005/08/004
[34] Ashtekar A and Das S 2000 Asymptotically Anti-de Sitter space-times: conserved quantities Class. Quantum Grav.17 L17 · Zbl 0943.83023
[35] Henningson M and Skenderis K 1998 The holographic weyl anomaly J. High Energ. Phys.JHEP07(1998) 023 · Zbl 0958.81083 · doi:10.1088/1126-6708/1998/07/023
[36] Miskovic O and Olea R 2009 Topological regularization and self-duality in four-dimensional anti-de Sitter gravity Phys. Rev. D 79 124020 · doi:10.1103/PhysRevD.79.124020
[37] Jatkar D P, Kofinas G, Miskovic O and Olea R 2014 Conformal mass in AdS gravity Phys. Rev. D 89 124010 · doi:10.1103/PhysRevD.89.124010
[38] Ashtekar A and Magnon A 1984 From i0 to the 3+1 description of spatial infinity J. Math. Phys.25 2682 · Zbl 0559.53044 · doi:10.1063/1.526500
[39] Mann R B, Marolf D and Virmani A 2006 Covariant counterterms and conserved charges in asymptotically flat spacetimes Class. Quantum Grav.23 6357 · Zbl 1117.83031 · doi:10.1088/0264-9381/23/22/017
[40] Bunster C, Gomberoff A and Prez A 2018 Regge-Teitelboim analysis of the symmetries of electromagnetic and gravitational fields on asymptotically null spacelike surfaces (arXiv:1805.03728 [hep-th])
[41] Deser S and Tekin B 2003 Energy in generic higher curvature gravity theories Phys. Rev. D 67 084009 · doi:10.1103/PhysRevD.67.084009
[42] Hajian K and Sheikh-Jabbari M M 2016 Solution phase space and conserved charges: a general formulation for charges associated with exact symmetries Phys. Rev. D 93 044074 · doi:10.1103/PhysRevD.93.044074
[43] Hajian K 2016 Conserved charges and first law of thermodynamics for Kerr – de Sitter black holes Gen. Relativ. Gravit.48 114 · Zbl 1381.83024 · doi:10.1007/s10714-016-2108-4
[44] Deser S, Kanik I and Tekin B 2005 Conserved charges of higher D Kerr-AdS spacetimes Class. Quantum Grav.22 3383 · Zbl 1135.83009 · doi:10.1088/0264-9381/22/17/001
[45] Wald R M 1984 General Relativity (Chicago, IL: Chicago University Press) · Zbl 0549.53001 · doi:10.7208/chicago/9780226870373.001.0001
[46] Carter B 1968 Hamilton-Jacobi and Schrodinger separable solutions of Einstein’s equations Commun. Math. Phys.10 280 · Zbl 0162.59302 · doi:10.1007/BF03399503
[47] Akcay S and Matzner R A 2011 Kerr – de Sitter universe Class. Quantum Grav.28 085012 · Zbl 1216.83033 · doi:10.1088/0264-9381/28/8/085012
[48] Hawking S W and Reall H S 2000 Charged and rotating AdS black holes and their CFT duals Phys. Rev. D 61 024014 · doi:10.1103/PhysRevD.61.024014
[49] Gibbons G W, Lu H, Page D N and Pope C N 2005 The general Kerr – de Sitter metrics in all dimensions J. Geom. Phys.53 49 · Zbl 1069.83003 · doi:10.1016/j.geomphys.2004.05.001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.