Abstract
A comprehensive analysis is presented based exclusively on near-horizon data to determine the attractor equations and the entropy of BPS black holes and rings in five space-time dimensions, for a Lagrangian invariant under eight supersymmetries with higher-derivative couplings. For spinning black holes the results only partially agree with the results of previous work, where often additional input was used beyond the near-horizon behaviour. A number of discrepancies remains, for example, pertaining to small black holes and to large spinning black holes, which are related to the presence of the higher-derivative couplings. Arguments are presented to explain some of them. For the black rings, the analysis is intricate due to the presence of Chern-Simons terms and due to the fact that the gauge fields are not globally defined. The contributions from the higher-derivative couplings take a systematic form in line with expectations based on a variety of arguments.
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References
S. Ferrara, R. Kallosh and A. Strominger, N=2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072] [SPIRES].
A. Strominger, Macroscopic Entropy of N = 2 Extremal Black Holes, Phys. Lett. B 383 (1996) 39 [hep-th/9602111] [SPIRES].
S. Ferrara and R. Kallosh, Supersymmetry and Attractors, Phys. Rev. D 54 (1996) 1514 [hep-th/9602136] [SPIRES].
G.L. Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black-hole entropy, Phys. Lett. B 451 (1999) 309 [hep-th/9812082] [SPIRES].
J.C. Breckenridge, R.C. Myers, A.W. Peet and C. Vafa, D-branes and spinning black holes, Phys. Lett. B 391 (1997) 93 [hep-th/9602065] [SPIRES].
J.P. Gauntlett, R.C. Myers and P.K. Townsend, Black holes of D = 5 supergravity, Class. Quant. Grav. 16 (1999) 1 [hep-th/9810204] [SPIRES].
H. Elvang, R. Emparan, D. Mateos and H.S. Reall, A supersymmetric black ring, Phys. Rev. Lett. 93 (2004) 211302 [hep-th/0407065] [SPIRES].
J.P. Gauntlett, J.B. Gutowski, C.M. Hull, S. Pakis and H.S. Reall, All supersymmetric solutions of minimal supergravity in five dimensions, Class. Quant. Grav. 20 (2003) 4587 [hep-th/0209114] [SPIRES].
J.P. Gauntlett and J.B. Gutowski, General concentric black rings, Phys. Rev. D 71 (2005) 045002 [hep-th/0408122] [SPIRES].
P. Kraus and F. Larsen, Attractors and black rings, Phys. Rev. D 72 (2005) 024010 [hep-th/0503219] [SPIRES].
K. Goldstein and R.P. Jena, One entropy function to rule them all, JHEP 11 (2007) 049 [hep-th/0701221] [SPIRES].
K. Hanaki, K. Ohashi and Y. Tachikawa, Comments on charges and near-horizon data of black rings, JHEP 12 (2007) 057 [arXiv:0704.1819] [SPIRES].
K. Hanaki, K. Ohashi and Y. Tachikawa, Supersymmetric Completion of an R 2 Term in Five- Dimensional Supergravity, Prog. Theor. Phys. 117 (2007) 533 [hep-th/0611329] [SPIRES].
P. Kraus and F. Larsen, Microscopic Black Hole Entropy in Theories with Higher Derivatives, JHEP 09 (2005) 034 [hep-th/0506176] [SPIRES].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, 5D Black Holes and Strings with Higher Derivatives, JHEP 06 (2007) 007 [hep-th/0703087] [SPIRES].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, Precision entropy of spinning black holes, JHEP 09 (2007) 003 [arXiv:0705.1847] [SPIRES].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, String Theory Effects on Five-Dimensional Black Hole Physics, Int. J. Mod. Phys. A 23 (2008) 613 [arXiv:0801.1863] [SPIRES].
A. Sen, Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity, JHEP 09 (2005) 038 [hep-th/0506177] [SPIRES].
N. Banerjee, I. Mandal and A. Sen, Black Hole Hair Removal, JHEP 07 (2009) 091 [arXiv:0901.0359] [SPIRES].
E. Lozano-Tellechea, P. Meessen and T. Ortín, On D = 4, 5, 6 vacua with 8 supercharges, Class. Quant. Grav. 19 (2002) 5921 [hep-th/0206200] [SPIRES].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038] [SPIRES].
T. Jacobson, G. Kang and R.C. Myers, On black hole entropy, Phys. Rev. D 49 (1994) 6587 [gr-qc/9312023] [SPIRES].
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] [SPIRES].
Y. Tachikawa, Black hole entropy in the presence of Chern-Simons terms, Class. Quant. Grav. 24 (2007) 737 [hep-th/0611141] [SPIRES].
D. Marolf, Chern-Simons terms and the three notions of charge, hep-th/0006117 [SPIRES].
C. Vafa, Black holes and Calabi-Yau threefolds, Adv. Theor. Math. Phys. 2 (1998) 207 [hep-th/9711067] [SPIRES].
M.-x. Huang, A. Klemm, M. Mariño and A. Tavanfar, Black Holes and Large Order Quantum Geometry, Phys. Rev. D 79 (2009) 066001 [arXiv:0704.2440] [SPIRES].
I. Bena and P. Kraus, Microscopic description of black rings in AdS/CFT, JHEP 12 (2004) 070 [hep-th/0408186] [SPIRES].
M. Cyrier, M. Guica, D. Mateos and A. Strominger, Microscopic entropy of the black ring, Phys. Rev. Lett. 94 (2005) 191601 [hep-th/0411187] [SPIRES].
A. Castro and S. Murthy, Corrections to the statistical entropy of five dimensional black holes, JHEP 06 (2009) 024 [arXiv:0807.0237] [SPIRES].
N. Banerjee, Subleading Correction to Statistical Entropy for BMPV Black Hole, Phys. Rev. D 79 (2009) 081501 [arXiv:0807.1314] [SPIRES].
J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [SPIRES].
P. Kraus and F. Larsen, Holographic gravitational anomalies, JHEP 01 (2006) 022 [hep-th/0508218] [SPIRES].
P. Kraus, Lectures on black holes and the AdS 3 /CFT 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [SPIRES].
I. Bena and P. Kraus, R 2 -corrections to black ring entropy, hep-th/0506015 [SPIRES].
M. Guica, L. Huang, W.W. Li and A. Strominger, R 2 corrections for 5D black holes and rings, JHEP 10 (2006) 036 [hep-th/0505188] [SPIRES].
D. Gaiotto, A. Strominger and X. Yin, New Connections Between 4D and 5D Black Holes, JHEP 02 (2006) 024 [hep-th/0503217] [SPIRES].
K. Behrndt, G. Lopes Cardoso and S. Mahapatra, Exploring the relation between 4D and 5D BPS solutions, Nucl. Phys. B 732 (2006) 200 [hep-th/0506251] [SPIRES].
K. Goldstein and S. Katmadas, Almost BPS black holes, JHEP 05 (2009) 058 [arXiv:0812.4183] [SPIRES].
B. de Wit, J. W. van Holten and A. Van Proeyen, Transformation Rules Of N=2 Supergravity Multiplets, Nucl. Phys. B 167 (1980) 186 [SPIRES].
B. de Wit, J.W. van Holten and A. Van Proeyen, Structure of N=2 supergravity, Nucl. Phys. B 184 (1981) 77 [SPIRES].
B. de Wit and A. Van Proeyen, Potentials and symmetries of general gauged N=2 supergravity: Yang-Mills models, Nucl. Phys. B 245 (1984) 89 [SPIRES].
B. de Wit, P.G. Lauwers and A. Van Proeyen, Lagrangians of N=2 Supergravity - Matter Systems, Nucl. Phys. B 255 (1985) 569 [SPIRES].
M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Properties of Conformal Supergravity, Phys. Rev. D 17 (1978) 3179 [SPIRES].
M. Kaku and P.K. Townsend, Poincaré supergravity as broken conformal supergravity, Phys. Lett. B 76 (1978) 54 [SPIRES].
T. Kugo and S. Uehara, Conformal and Poincaré Tensor calculi in N = 1 supergravity, Nucl. Phys. B 226 (1983) 49 [SPIRES].
E. Bergshoeff, E. Sezgin and A. Van Proeyen, Superconformal tensor calculus and matter couplings in six-dimensions, Nucl. Phys. B 264 (1986) 653 [SPIRES].
E. Bergshoeff et al., Weyl multiplets of N = 2 conformal supergravity in five dimensions, JHEP 06 (2001) 051 [hep-th/0104113] [SPIRES].
T. Fujita and K. Ohashi, Superconformal tensor calculus in five dimensions, Prog. Theor. Phys. 106 (2001) 221 [hep-th/0104130] [SPIRES].
E. Bergshoeff et al., N = 2 supergravity in five dimensions revisited, Class. Quant. Grav. 21 (2004) 3015 [hep-th/0403045] [SPIRES].
B. de Wit, B. Kleijn and S. Vandoren, Superconformal hypermultiplets, Nucl. Phys. B 568 (2000) 475 [hep-th/9909228] [SPIRES].
B. de Wit, M. Roček and S. Vandoren, Hypermultiplets, hyperKähler cones and quaternion-Kähler geometry, JHEP 02 (2001) 039 [hep-th/0101161] [SPIRES].
A.F. Swann, Hyperkähler and quaternionic Kähler geometry, Math. Ann. 289 (1991) 421.
G. Lopes Cardoso, B. de Wit, J. Käppeli and T. Mohaupt, Stationary BPS solutions in N = 2 supergravity with R 2 interactions, JHEP 12 (2000) 019 [hep-th/0009234] [SPIRES].
P. Krtous, D. Kubiznak, D.N. Page and V.P. Frolov, Killing-Yano tensors, rank-2 Killing tensors and conserved quantities in higher dimensions, JHEP 02 (2007) 004 [hep-th/0612029] [SPIRES].
M. Henneaux and C. Teitelboim, Quantization of topological mass in the presence of a magnetic pole, Phys. Rev. Lett. 56 (1986) 689 [SPIRES].
X. Bekaert and A. Gomberoff, Quantization of the Chern-Simons coupling constant, JHEP 01 (2003) 054 [hep-th/0212099] [SPIRES].
R. Emparan and H.S. Reall, Black rings, Class. Quant. Grav. 23 (2006) R169 [hep-th/0608012] [SPIRES].
X. Bekaert, Issues in electric-magnetic duality, hep-th/0209169 [SPIRES].
N.V. Suryanarayana and M.C. Wapler, Charges from Attractors, Class. Quant. Grav. 24 (2007) 5047 [arXiv:0704.0955] [SPIRES].
K. Copsey and G.T. Horowitz, The role of dipole charges in black hole thermodynamics, Phys. Rev. D 73 (2006) 024015 [hep-th/0505278] [SPIRES].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Macroscopic entropy formulae and non-holomorphic corrections for supersymmetric black holes, Nucl. Phys. B 567 (2000) 87 [hep-th/9906094] [SPIRES].
B. de Wit, V. Kaplunovsky, J. Louis and D. Lüst, Perturbative couplings of vector multiplets in N=2 heterotic string vacua, Nucl. Phys. B 451 (1995) 53 [hep-th/9504006] [SPIRES].
B. de Wit and F. Saueressig, Off-shell N = 2 tensor supermultiplets, JHEP 09 (2006) 062 [hep-th/0606148] [SPIRES].
H. Elvang, R. Emparan, D. Mateos and H.S. Reall, Supersymmetric 4D rotating black holes from 5D black rings, JHEP 08 (2005) 042 [hep-th/0504125] [SPIRES].
M. Bertolini and M. Trigiante, Microscopic entropy of the most general four-dimensional BPS black hole, JHEP 10 (2000) 002 [hep-th/0008201] [SPIRES].
I. Bena, P. Kraus and N.P. Warner, Black rings in Taub-NUT, Phys. Rev. D 72 (2005) 084019 [hep-th/0504142] [SPIRES].
I. Bena and N.P. Warner, One ring to rule them all ... and in the darkness bind them?, Adv. Theor. Math. Phys. 9 (2005) 667 [hep-th/0408106] [SPIRES].
B. de Wit and J.W. van Holten, Multiplets of linearized SO(2) supergravity, Nucl. Phys. B 155 (1979) 530.
E. Bergshoeff, M. de Roo and B. de Wit, Extended Conformal Supergravity, Nucl. Phys. B 182 (1981) 173 [SPIRES].
P.S. Howe and U. Lindstrom, The supercurrent in five-dimensions, Phys. Lett. B 103 (1981) 422 [SPIRES].
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de Wit, B., Katmadas, S. Near-horizon analysis of D=5 BPS black holes and rings. J. High Energ. Phys. 2010, 56 (2010). https://doi.org/10.1007/JHEP02(2010)056
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DOI: https://doi.org/10.1007/JHEP02(2010)056