Abstract
Within class of generic black holes there are extremal black holes (with vanishing Hawking temperature T) and vanishing horizon area A h , but with finite A h /T ratio, the Extremal Vanishing Horizon (EVH) black holes. We study the near horizon limit of a four dimensional EVH black hole solution to a generic (gauged) Einstein-Maxwell dilaton theory and show that in the near horizon limit they develop a throat which is a pinching orbifold limit of AdS3. This is an extension of the well known result for extremal black holes the near horizon limit of which contains an AdS2 throat. We show that in the near EVH near horizon limit the pinching AdS3 factor turns to a pinching BTZ black hole and that this near horizon limit is indeed a decoupling limit. We argue that the pinching AdS3 or BTZ orbifold is resolved if the near horizon limit is accompanied by taking the 4d Newton constant G 4 to zero such that the Bekenstein-Hawking entropy S = A h /(4G 4) remains finite. We propose that in this limit the near horizon EVH black hole is dual to a 2d CFT. We provide pieces of evidence in support of the EVH/CFT correspondence and comment on its connection to the Kerr/CFT proposal and speculation show the EVH/CFT maybe used to study generic e.g. Schwarzchild-type black holes.
Similar content being viewed by others
References
A. Strominger and C. Vafa, Microscopic Origin of the Bekenstein-Hawking Entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [SPIRES].
I. Mandal and A. Sen, Black Hole Microstate Counting and its Macroscopic Counterpart, Class. Quant. Grav. 27 (2010) 214003 [arXiv:1008.3801] [SPIRES].
A. Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [SPIRES].
J. Simon, Extremal black holes, Holography & Coarse graining, Int. J. Mod. Phys. A 26 (2011) 1903 [arXiv:1106.0116] [SPIRES].
H.K. Kunduri and J. Lucietti, A classification of near-horizon geometries of extremal vacuum black holes, J. Math. Phys. 50 (2009) 082502 [arXiv:0806.2051] [SPIRES].
H.K. Kunduri, J. Lucietti and H.S. Reall, Supersymmetric multi-charge AdS 5 black holes, JHEP 04 (2006) 036 [hep-th/0601156] [SPIRES].
A. Sen, Quantum Entropy Function from AdS 2/CFT 1 Correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [SPIRES].
A. Sen, State Operator Correspondence and Entanglement in AdS 2/CFT 1, arXiv:1101.4254 [SPIRES].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [SPIRES].
H.Lü, J. Mei and C.N. Pope, Kerr/CFT Correspondence in Diverse Dimensions, JHEP 04 (2009) 054 [arXiv:0811.2225] [SPIRES].
T. Hartman, K. Murata, T. Nishioka and A. Strominger, CFT Duals for Extreme Black Holes, JHEP 04 (2009) 019 [arXiv:0811.4393] [SPIRES].
J.-J. Peng and S.-Q. Wu, Extremal Kerr/CFT correspondence of five-dimensional rotating (charged) black holes with squashed horizons, Nucl. Phys. B 828 (2010) 273 [arXiv:0911.5070] [SPIRES].
R. Li, M.-F. Li and J.-R. Ren, Entropy of Kaluza-Klein Black Hole from Kerr/CFT Correspondence, Phys. Lett. B 691 (2010) 249 [arXiv:1004.5335] [SPIRES].
B. Chen and J. Long, On Holographic description of the Kerr-Newman-AdS-dS black holes, JHEP 08 (2010) 065 [arXiv:1006.0157] [SPIRES].
V. Balasubramanian, J. de Boer, M.M. Sheikh-Jabbari and J. Simon, What is a chiral 2d CFT? And what does it have to do with extremal black holes?, JHEP 02 (2010) 017 [arXiv:0906.3272] [SPIRES].
O.J.C. Dias, H.S. Reall and J.E. Santos, Kerr-CFT and gravitational perturbations, JHEP 08 (2009) 101 [arXiv:0906.2380] [SPIRES].
A.J. Amsel, G.T. Horowitz, D. Marolf and M.M. Roberts, No Dynamics in the Extremal Kerr Throat, JHEP 09 (2009) 044 [arXiv:0906.2376] [SPIRES].
J. de Boer, M.M. Sheikh-Jabbari and J. Simon, Near Horizon Limits of Massless BTZ and Their CFT Duals, Class. Quant. Grav. 28 (2011) 175012 [arXiv:1011.1897] [SPIRES].
J.M. Bardeen and G.T. Horowitz, The extreme Kerr throat geometry: A vacuum analog of AdS 2 × S 2, Phys. Rev. D 60 (1999) 104030 [hep-th/9905099] [SPIRES].
V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, Entropy of near-extremal black holes in AdS 5, JHEP 05 (2008) 067 [arXiv:0707.3601] [SPIRES].
R. Fareghbal, C.N. Gowdigere, A.E. Mosaffa and M.M. Sheikh-Jabbari, Nearing Extremal Intersecting Giants and New Decoupled Sectors in N = 4 SYM, JHEP 08 (2008) 070 [arXiv:0801.4457] [SPIRES].
R. Fareghbal, C.N. Gowdigere, A.E. Mosaffa and M.M. Sheikh-Jabbari, Nearing 11 d Extremal Intersecting Giants and New Decoupled Sectors in D = 3, 6 SCFT’s, Phys. Rev. D 81 (2010) 046005 [arXiv:0805.0203] [SPIRES].
T. Azeyanagi, N. Ogawa and S. Terashima, Emergent AdS 3 in the Zero Entropy Extremal Black Holes, JHEP 03 (2011) 004 [arXiv:1010.4291] [SPIRES].
T. Azeyanagi, N. Ogawa and S. Terashima, On Non-Chiral Extension of Kerr/CFT, JHEP 06 (2011) 081 [arXiv:1102.3423] [SPIRES].
K. Goldstein, N. Iizuka, R.P. Jena and S.P. Trivedi, Non-supersymmetric attractors, Phys. Rev. D 72 (2005) 124021 [hep-th/0507096] [SPIRES].
A. Sen, Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity, JHEP 09 (2005) 038 [hep-th/0506177] [SPIRES].
D. Astefanesei, K. Goldstein, R.P. Jena, A. Sen and S.P. Trivedi, Rotating attractors, JHEP 10 (2006) 058 [hep-th/0606244] [SPIRES].
D. Astefanesei and H. Yavartanoo, Stationary black holes and attractor mechanism, Nucl. Phys. B 794 (2008) 13 [arXiv:0706.1847] [SPIRES].
P. Kraus and F. Larsen, Microscopic Black Hole Entropy in Theories with Higher Derivatives, JHEP 09 (2005) 034 [hep-th/0506176] [SPIRES].
P. Kraus and F. Larsen, Holographic gravitational anomalies, JHEP 01 (2006) 022 [hep-th/0508218] [SPIRES].
H. Saida and J. Soda, Statistical entropy of BTZ black hole in higher curvature gravity, Phys. Lett. B 471 (2000) 358 [gr-qc/9909061] [SPIRES].
F. Loran, M.M. Sheikh-Jabbari and M. Vincon, Beyond Logarithmic Corrections to Cardy Formula, JHEP 01 (2011) 110 [arXiv:1010.3561] [SPIRES].
D. Rasheed, The Rotating dyonic black holes of Kaluza-Klein theory, Nucl. Phys. B 454 (1995) 379 [hep-th/9505038] [SPIRES].
T. Matos and C. Mora, Stationary dilatons with arbitrary electromagnetic field, Class. Quant. Grav. 14 (1997) 2331 [hep-th/9610013] [SPIRES].
F. Larsen, Rotating Kaluza-Klein black holes, Nucl. Phys. B 575 (2000) 211 [hep-th/9909102] [SPIRES].
R. Emparan and G.T. Horowitz, Microstates of a neutral black hole in M-theory, Phys. Rev. Lett. 97 (2006) 141601 [hep-th/0607023] [SPIRES].
R. Emparan and A. Maccarrone, Statistical Description of Rotating Kaluza-Klein Black Holes, Phys. Rev. D 75 (2007) 084006 [hep-th/0701150] [SPIRES].
W. Taylor, Adhering 0-branes to 6-branes and 8-branes, Nucl. Phys. B 508 (1997) 122 [hep-th/9705116] [SPIRES].
V. Jejjala and S. Nampuri, Cardy and Kerr, JHEP 02 (2010) 088 [arXiv:0909.1110] [SPIRES].
T. Azeyanagi, N. Ogawa and S. Terashima, Holographic Duals of Kaluza-Klein Black Holes, JHEP 04 (2009) 061 [arXiv:0811.4177] [SPIRES].
A. Sen, How does a fundamental string stretch its horizon?, JHEP 05 (2005) 059 [hep-th/0411255] [SPIRES].
A. Sen, Stretching the horizon of a higher dimensional small black hole, JHEP 07 (2005) 073 [hep-th/0505122] [SPIRES].
J. Camps, R. Emparan, P. Figueras, S. Giusto and A. Saxena, Black Rings in Taub-NUT and D0-D6 interactions, JHEP 02 (2009) 021 [arXiv:0811.2088] [SPIRES].
M. Cvetič et al., Embedding AdS black holes in ten and eleven dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [SPIRES].
M.J. Duff, Lectures on branes, black holes and anti-de Sitter space, hep-th/9912164 [SPIRES].
M. Alishahiha, H. Ita and Y. Oz, Graviton scattering on D6 branes with B fields, JHEP 06 (2000) 002 [hep-th/0004011] [SPIRES].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [SPIRES].
E.J. Martinec and W. McElgin, String theory on AdS orbifolds, JHEP 04 (2002) 029 [hep-th/0106171] [SPIRES].
M. Guica and A. Strominger, Microscopic Realization of the Kerr/CFT Correspondence, JHEP 02 (2011) 010 [arXiv:1009.5039] [SPIRES].
G. Compere, W. Song and A. Virmani, Microscopics of Extremal Kerr from Spinning M5 Branes, arXiv:1010.0685 [SPIRES].
R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Ann. Phys. 172 (1986) 304 [SPIRES].
J. de Boer, M.M. Sheikh-Jabbari and J. Simon, work in progress.
J. Simón, M.M. Sheikh-Jabbari, unplublished notes on 5d EVH blackholes.
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Charged rotating black holes in four-dimensional gauged and ungauged supergravities, Nucl. Phys. B 717 (2005) 246 [hep-th/0411045] [SPIRES].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Non-extremal charged rotating black holes in seven-dimensional gauged supergravity, Phys. Lett. B 626 (2005) 215 [hep-th/0412094] [SPIRES].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity, Phys. Rev. Lett. 95 (2005) 161301 [hep-th/0506029] [SPIRES].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Non-extremal rotating black holes in five-dimensional gauged supergravity, Phys. Lett. B 644 (2007) 192 [hep-th/0606213] [SPIRES].
J. Mei and C.N. Pope, New Rotating Non-Extremal Black Holes in D = 5 Maximal Gauged Supergravity, Phys. Lett. B 658 (2007) 64 [arXiv:0709.0559] [SPIRES].
W. Chen, H. Lü and C.N. Pope, Mass of rotating black holes in gauged supergravities, Phys. Rev. D 73 (2006) 104036 [hep-th/0510081] [SPIRES].
R. Emparan and H.S. Reall, Black Holes in Higher Dimensions, Living Rev. Rel. 11 (2008) 6 [arXiv:0801.3471] [SPIRES].
R. Emparan and P. Figueras, Multi-black rings and the phase diagram of higher-dimensional black holes, JHEP 11 (2010) 022 [arXiv:1008.3243] [SPIRES].
R. Emparan and H.S. Reall, A rotating black ring in five dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [SPIRES].
V. Balasubramanian, J. Parsons and S.F. Ross, States of a chiral 2d CFT, Class. Quant. Grav. 28 (2011) 045004 [arXiv:1011.1803] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1107.5705
Rights and permissions
About this article
Cite this article
Sheikh-Jabbari, M.M., Yavartanoo, H. EVH black holes, AdS3 throats and EVH/CFT proposal. J. High Energ. Phys. 2011, 13 (2011). https://doi.org/10.1007/JHEP10(2011)013
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2011)013