Abstract
We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute asymptotic symmetries in any Chern-Simons-like theory of gravity. We use this to show that the near horizon symmetry algebra consists of two \( \mathfrak{u} \)(1) current algebras and recover the surprisingly simple entropy formula S = 2π(J +0 + J −0 ), where J ±0 are zero mode charges of the current algebras. This provides the first example of a locally non-maximally symmetric configuration exhibiting this entropy law and thus non-trivial evidence for its universality.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
L. Susskind, Some speculations about black hole entropy in string theory, hep-th/9309145 [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
Y. Tachikawa, Black hole entropy in the presence of Chern-Simons terms, Class. Quant. Grav. 24 (2007) 737 [hep-th/0611141] [INSPIRE].
H. Afshar et al., Soft Heisenberg hair on black holes in three dimensions, Phys. Rev. D 93 (2016) 101503 [arXiv:1603.04824] [INSPIRE].
H. Afshar, D. Grumiller, W. Merbis, A. Perez, D. Tempo and R. Troncoso, Soft hairy horizons in three spacetime dimensions, Phys. Rev. D 95 (2017) 106005 [arXiv:1611.09783] [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Soft hair on black holes, Phys. Rev. Lett. 116 (2016) 231301 [arXiv:1601.00921] [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Superrotation charge and supertranslation hair on black holes, JHEP 05 (2017) 161 [arXiv:1611.09175] [INSPIRE].
L. Donnay, G. Giribet, H.A. Gonzalez and M. Pino, Supertranslations and superrotations at the black hole horizon, Phys. Rev. Lett. 116 (2016) 091101 [arXiv:1511.08687] [INSPIRE].
L. Donnay, G. Giribet, H.A. González and M. Pino, Extended symmetries at the black hole horizon, JHEP 09 (2016) 100 [arXiv:1607.05703] [INSPIRE].
M.R. Setare and H. Adami, The Heisenberg algebra as near horizon symmetry of the black flower solutions of Chern-Simons-like theories of gravity, Nucl. Phys. B 914 (2017) 220 [arXiv:1606.05260] [INSPIRE].
D. Grumiller, A. Perez, S. Prohazka, D. Tempo and R. Troncoso, Higher spin black holes with soft hair, JHEP 10 (2016) 119 [arXiv:1607.05360] [INSPIRE].
M. Ammon, D. Grumiller, S. Prohazka, M. Riegler and R. Wutte, Higher-spin flat space cosmologies with soft hair, JHEP 05 (2017) 031 [arXiv:1703.02594] [INSPIRE].
D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 black holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [Annals Phys. 281 (2000) 409] [INSPIRE].
O. Hohm, A. Routh, P.K. Townsend and B. Zhang, On the Hamiltonian form of 3D massive gravity, Phys. Rev. D 86 (2012) 084035 [arXiv:1208.0038] [INSPIRE].
E.A. Bergshoeff, O. Hohm, W. Merbis, A.J. Routh and P.K. Townsend, Chern-Simons-like gravity theories, Lect. Notes Phys. 892 (2015) 181 [arXiv:1402.1688] [INSPIRE].
W. Merbis, Chern-Simons-like theories of gravity, Ph.D. thesis, Groningen U., Groningen The Netherlands, (2014) [arXiv:1411.6888] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive gravity in three dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, More on massive 3D gravity, Phys. Rev. D 79 (2009) 124042 [arXiv:0905.1259] [INSPIRE].
E.A. Bergshoeff, S. de Haan, O. Hohm, W. Merbis and P.K. Townsend, Zwei-dreibein gravity: a two-frame-field model of 3D massive gravity, Phys. Rev. Lett. 111 (2013) 111102 [Erratum ibid. 111 (2013) 259902] [arXiv:1307.2774] [INSPIRE].
E. Bergshoeff, O. Hohm, W. Merbis, A.J. Routh and P.K. Townsend, Minimal massive 3D gravity, Class. Quant. Grav. 31 (2014) 145008 [arXiv:1404.2867] [INSPIRE].
H.R. Afshar, E.A. Bergshoeff and W. Merbis, Extended massive gravity in three dimensions, JHEP 08 (2014) 115 [arXiv:1405.6213] [INSPIRE].
H.R. Afshar, E.A. Bergshoeff and W. Merbis, Interacting spin-2 fields in three dimensions, JHEP 01 (2015) 040 [arXiv:1410.6164] [INSPIRE].
M.R. Setare, On the generalized minimal massive gravity, Nucl. Phys. B 898 (2015) 259 [arXiv:1412.2151] [INSPIRE].
H. Adami, M.R. Setare, T.C. Sisman and B. Tekin, Conserved charges in extended theories of gravity, arXiv:1710.07252 [INSPIRE].
M.R. Setare and H. Adami, Near horizon geometry of warped black holes in generalized minimal massive gravity, arXiv:1711.08344 [INSPIRE].
T. Evrard, Conditions au bord á l’horizon et symétries infini-dimensionelles (in French), S. Detournay advisor, (2017).
A. Garcia, F.W. Hehl, C. Heinicke and A. Macias, The Cotton tensor in Riemannian space-times, Class. Quant. Grav. 21 (2004) 1099 [gr-qc/0309008] [INSPIRE].
S. Ertl, D. Grumiller and N. Johansson, All stationary axi-symmetric local solutions of topologically massive gravity, Class. Quant. Grav. 27 (2010) 225021 [arXiv:1006.3309] [INSPIRE].
D.D.K. Chow, C.N. Pope and E. Sezgin, Classification of solutions in topologically massive gravity, Class. Quant. Grav. 27 (2010) 105001 [arXiv:0906.3559] [INSPIRE].
I. Vuorio, Topologically massive planar universe, Phys. Lett. B 163 (1985) 91 [INSPIRE].
R. Percacci, P. Sodano and I. Vuorio, Topologically massive planar universes with constant twist, Annals Phys. 176 (1987) 344 [INSPIRE].
Y. Nutku, Exact solutions of topologically massive gravity with a cosmological constant, Class. Quant. Grav. 10 (1993) 2657 [INSPIRE].
M. Gürses, Perfect fluid sources in 2 + 1 dimensions, Class. Quant. Grav. 11 (1994) 2585 [INSPIRE].
A. Bouchareb and G. Clement, Black hole mass and angular momentum in topologically massive gravity, Class. Quant. Grav. 24 (2007) 5581 [arXiv:0706.0263] [INSPIRE].
G. Clement, Warped AdS 3 black holes in new massive gravity, Class. Quant. Grav. 26 (2009) 105015 [arXiv:0902.4634] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [Erratum ibid. D 88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
G. Compere and S. Detournay, Boundary conditions for spacelike and timelike warped AdS 3 spaces in topologically massive gravity, JHEP 08 (2009) 092 [arXiv:0906.1243] [INSPIRE].
M. Henneaux, C. Martinez and R. Troncoso, Asymptotically warped anti-de Sitter spacetimes in topologically massive gravity, Phys. Rev. D 84 (2011) 124016 [arXiv:1108.2841] [INSPIRE].
M. Bañados, Global charges in Chern-Simons field theory and the (2 + 1) black hole, Phys. Rev. D 52 (1996) 5816 [hep-th/9405171] [INSPIRE].
G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B 633 (2002) 3 [hep-th/0111246] [INSPIRE].
A. Achucarro and P.K. Townsend, A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].
E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
T. Regge and C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Annals Phys. 88 (1974) 286 [INSPIRE].
M. Henneaux, A. Perez, D. Tempo and R. Troncoso, Chemical potentials in three-dimensional higher spin anti-de Sitter gravity, JHEP 12 (2013) 048 [arXiv:1309.4362] [INSPIRE].
P. Kraus and F. Larsen, Holographic gravitational anomalies, JHEP 01 (2006) 022 [hep-th/0508218] [INSPIRE].
P. Kraus, Lectures on black holes and the AdS 3 /CFT 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [INSPIRE].
G. Compere and S. Detournay, Semi-classical central charge in topologically massive gravity, Class. Quant. Grav. 26 (2009) 012001 [Erratum ibid. 26 (2009) 139801] [arXiv:0808.1911] [INSPIRE].
S. Detournay, T. Hartman and D.M. Hofman, Warped conformal field theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].
E. Halyo, Rindler energy is Wald entropy, arXiv:1403.2333 [INSPIRE].
H. Afshar, D. Grumiller and M.M. Sheikh-Jabbari, Near horizon soft hair as microstates of three dimensional black holes, Phys. Rev. D 96 (2017) 084032 [arXiv:1607.00009] [INSPIRE].
M.M. Sheikh-Jabbari and H. Yavartanoo, Horizon fluffs: near horizon soft hairs as microstates of generic AdS 3 black holes, Phys. Rev. D 95 (2017) 044007 [arXiv:1608.01293] [INSPIRE].
H. Afshar, D. Grumiller, M.M. Sheikh-Jabbari and H. Yavartanoo, Horizon fluff, semi-classical black hole microstates — log-corrections to BTZ entropy and black hole/particle correspondence, JHEP 08 (2017) 087 [arXiv:1705.06257] [INSPIRE].
D. Grumiller, A. Perez, D. Tempo and R. Troncoso, Log corrections to entropy of three dimensional black holes with soft hair, JHEP 08 (2017) 107 [arXiv:1705.10605] [INSPIRE].
A. Sen, Logarithmic corrections to Schwarzschild and other non-extremal black hole entropy in different dimensions, JHEP 04 (2013) 156 [arXiv:1205.0971] [INSPIRE].
H. Gonzalez, D. Grumiller, W. Merbis and R. Wutte, New entropy formula for Kerr black holes, in Proceedings of the 13th International Conference on Gravitation, Astrophysics, and Cosmology, (2017) [EPJ Web Conf. 168 (2018) 01009] [arXiv:1709.09667] [INSPIRE].
K. Hajian, M.M. Sheikh-Jabbari and H. Yavartanoo, Fluffing extreme Kerr, arXiv:1708.06378 [INSPIRE].
C. Bunster, M. Henneaux, A. Perez, D. Tempo and R. Troncoso, Generalized black holes in three-dimensional spacetime, JHEP 05 (2014) 031 [arXiv:1404.3305] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1711.07975
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Grumiller, D., Hacker, P. & Merbis, W. Soft hairy warped black hole entropy. J. High Energ. Phys. 2018, 10 (2018). https://doi.org/10.1007/JHEP02(2018)010
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2018)010