Abstract
We consider perturbative solutions in Einstein gravity with higher-derivative extensions and address some subtle issues of taking extremal limit. As a concrete new result, we construct the perturbative rotating black hole in five dimensions with equal angular momenta J and general mass M in Einstein-Gauss-Bonnet gravity, up to and including the linear order of the standard Gauss-Bonnet coupling constant α. We obtain the near horizon structure of the near extremal solution, with the blackening factor of the order α. In the extremal limit, the mass-angular momentum relation reduces to \( M=\frac{3}{2}{\pi}^{\frac{1}{3}}{J}^{\frac{2}{3}}+\pi \alpha \). The positive sign of the α-correction implies that the centrifugal repulsion associated with rotations becomes weaker than the gravitational attraction under the unitary requirement for the Gauss-Bonnet term.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K.S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
K.S. Stelle, Classical Gravity with Higher Derivatives, Gen. Rel. Grav. 9 (1978) 353 [INSPIRE].
D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498 [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
C. Cheung, J. Liu and G.N. Remmen, Proof of the Weak Gravity Conjecture from Black Hole Entropy, JHEP 10 (2018) 004 [arXiv:1801.08546] [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The String landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
Y. Hamada, T. Noumi and G. Shiu, Weak Gravity Conjecture from Unitarity and Causality, Phys. Rev. Lett. 123 (2019) 051601 [arXiv:1810.03637] [INSPIRE].
H.S. Reall and J.E. Santos, Higher derivative corrections to Kerr black ole thermodynamics, JHEP 04 (2019) 021 [arXiv:1901.11535] [INSPIRE].
C. Cheung, J. Liu and G.N. Remmen, Entropy Bounds on Effective Field Theory from Rotating Dyonic Black Holes, Phys. Rev. D 100 (2019) 046003 [arXiv:1903.09156] [INSPIRE].
L. Aalsma, A. Cole and G. Shiu, Weak Gravity Conjecture, Black Hole Entropy, and Modular Invariance, JHEP 08 (2019) 022 [arXiv:1905.06956] [INSPIRE].
G.J. Loges, T. Noumi and G. Shiu, Thermodynamics of 4D Dilatonic Black Holes and the Weak Gravity Conjecture, Phys. Rev. D 102 (2020) 046010 [arXiv:1909.01352] [INSPIRE].
G. Goon and R. Penco, Universal Relation between Corrections to Entropy and Extremality, Phys. Rev. Lett. 124 (2020) 101103 [arXiv:1909.05254] [INSPIRE].
S. Cremonini, C.R.T. Jones, J.T. Liu and B. McPeak, Higher-Derivative Corrections to Entropy and the Weak Gravity Conjecture in Anti-de Sitter Space, JHEP 09 (2020) 003 [arXiv:1912.11161] [INSPIRE].
W.-M. Chen, Y.-T. Huang, T. Noumi and C. Wen, Unitarity bounds on charged/neutral state mass ratios, Phys. Rev. D 100 (2019) 025016 [arXiv:1901.11480] [INSPIRE].
B. Bellazzini, M. Lewandowski and J. Serra, Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity, Phys. Rev. Lett. 123 (2019) 251103 [arXiv:1902.03250] [INSPIRE].
M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].
J.T. Liu and P. Szepietowski, Higher derivative corrections to R-charged AdS5 black holes and field redefinitions, Phys. Rev. D 79 (2009) 084042 [arXiv:0806.1026] [INSPIRE].
S. Cremonini, J.T. Liu and P. Szepietowski, Higher Derivative Corrections to R-charged Black Holes: Boundary Counterterms and the Mass-Charge Relation, JHEP 03 (2010) 042 [arXiv:0910.5159] [INSPIRE].
P. Bueno, P.A. Cano, J. Moreno and A. Murcia, All higher-curvature gravities as Generalized quasi-topological gravities, JHEP 11 (2019) 062 [arXiv:1906.00987] [INSPIRE].
G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].
H.-S. Liu, Z.-F. Mai, Y.-Z. Li and H. Lü, Quasi-topological Electromagnetism: Dark Energy, Dyonic Black Holes, Stable Photon Spheres and Hidden Electromagnetic Duality, Sci. China Phys. Mech. Astron. 63 (2020) 240411 [arXiv:1907.10876] [INSPIRE].
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
C. Cheung and G.N. Remmen, Positivity of Curvature-Squared Corrections in Gravity, Phys. Rev. Lett. 118 (2017) 051601 [arXiv:1608.02942] [INSPIRE].
D.G. Boulware and S. Deser, String Generated Gravity Models, Phys. Rev. Lett. 55 (1985) 2656 [INSPIRE].
D.L. Wiltshire, Spherically Symmetric Solutions of Einstein-Maxwell Theory With a Gauss-Bonnet Term, Phys. Lett. B 169 (1986) 36 [INSPIRE].
R.-G. Cai and K.-S. Soh, Topological black holes in the dimensionally continued gravity, Phys. Rev. D 59 (1999) 044013 [gr-qc/9808067] [INSPIRE].
R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133] [INSPIRE].
M. Cvetič, S. Nojiri and S.D. Odintsov, Black hole thermodynamics and negative entropy in de Sitter and anti-de Sitter Einstein-Gauss-Bonnet gravity, Nucl. Phys. B 628 (2002) 295 [hep-th/0112045] [INSPIRE].
X.-H. Feng and H. Lü, Higher-Derivative Gravity with Non-minimally Coupled Maxwell Field, Eur. Phys. J. C 76 (2016) 178 [arXiv:1512.09153] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
X.-H. Feng, H.-S. Liu, H. Lü and C.N. Pope, Black Hole Entropy and Viscosity Bound in Horndeski Gravity, JHEP 11 (2015) 176 [arXiv:1509.07142] [INSPIRE].
X.-H. Feng, H.-S. Liu, H. Lü and C.N. Pope, Thermodynamics of Charged Black Holes in Einstein-Horndeski-Maxwell Theory, Phys. Rev. D 93 (2016) 044030 [arXiv:1512.02659] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038] [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].
P.A. Cano, S. Chimento, R. Linares, T. Ortín and P.F. Ramírez, α′ corrections of Reissner-Nordström black holes, JHEP 02 (2020) 031 [arXiv:1910.14324] [INSPIRE].
H.-S. Liu, H. Lü and Z.-L. Wang, f (R) Theories of Supergravities and Pseudo-supergravities, JHEP 04 (2012) 072 [arXiv:1201.2417] [INSPIRE].
R.P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett. 11 (1963) 237 [INSPIRE].
B. Carter, Hamilton-Jacobi and Schrödinger separable solutions of Einstein’s equations, Commun. Math. Phys. 10 (1968) 280 [INSPIRE].
R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys. 172 (1986) 304 [INSPIRE].
S.W. Hawking, C.J. Hunter and M. Taylor, Rotation and the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 064005 [hep-th/9811056] [INSPIRE].
G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, Rotating black holes in higher dimensions with a cosmological constant, Phys. Rev. Lett. 93 (2004) 171102 [hep-th/0409155] [INSPIRE].
G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, The General Kerr-de Sitter metrics in all dimensions, J. Geom. Phys. 53 (2005) 49 [hep-th/0404008] [INSPIRE].
W.-M. Chen, H. Lü and C.N. Pope, General Kerr-NUT-AdS metrics in all dimensions, Class. Quant. Grav. 23 (2006) 5323 [hep-th/0604125] [INSPIRE].
H. Lü, J. Mei and C.N. Pope, New Black Holes in Five Dimensions, Nucl. Phys. B 806 (2009) 436 [arXiv:0804.1152] [INSPIRE].
R. Emparan and H.S. Reall, A Rotating black ring solution in five-dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [INSPIRE].
Y. Brihaye and E. Radu, Five-dimensional rotating black holes in Einstein-Gauss-Bonnet theory, Phys. Lett. B 661 (2008) 167 [arXiv:0801.1021] [INSPIRE].
Y. Brihaye, B. Kleihaus, J. Kunz and E. Radu, Rotating black holes with equal-magnitude angular momenta in d = 5 Einstein-Gauss-Bonnet theory, JHEP 11 (2010) 098 [arXiv:1010.0860] [INSPIRE].
Y. Brihaye and E. Radu, Five-dimensional rotating black holes in Einstein-Gauss-Bonnet theory, Phys. Lett. B 661 (2008) 167 [arXiv:0801.1021] [INSPIRE].
B. Kleihaus, J. Kunz and E. Radu, Rotating Black Holes in Dilatonic Einstein-Gauss-Bonnet Theory, Phys. Rev. Lett. 106 (2011) 151104 [arXiv:1101.2868] [INSPIRE].
R.-H. Yue, D.-C. Zou, T.-Y. Yu and Z.-Y. Yang, A new metric for rotating black holes in Gauss-Bonnet gravity, Chin. Phys. B 20 (2011) 050401 [arXiv:1107.2743] [INSPIRE].
M. Okounkova, Stability of Rotating Black Holes in Einstein Dilaton Gauss-Bonnet Gravity, Phys. Rev. D 100 (2019) 124054 [arXiv:1909.12251] [INSPIRE].
P.A. Cano and D. Pereñiguez, Extremal Rotating Black Holes in Einsteinian Cubic Gravity, Phys. Rev. D 101 (2020) 044016 [arXiv:1910.10721] [INSPIRE].
C. Adair, P. Bueno, P.A. Cano, R.A. Hennigar and R.B. Mann, Slowly rotating black holes in Einsteinian cubic gravity, Phys. Rev. D 102 (2020) 084001 [arXiv:2004.09598] [INSPIRE].
R.A. Konoplya and A. Zhidenko, Simply rotating higher dimensional black holes in Einstein-Gauss-Bonnet theory, Phys. Rev. D 102 (2020) 084030 [arXiv:2007.10116] [INSPIRE].
X.-H. Feng, W.-J. Geng and H. Lü, Time Machines and AdS Solitons with Negative Mass, Phys. Rev. D 95 (2017) 084013 [arXiv:1701.00006] [INSPIRE].
M. Cvetič, W.-J. Geng, H. Lü and C.N. Pope, BPS Kerr-AdS Time Machines, JHEP 07 (2018) 088 [arXiv:1801.08579] [INSPIRE].
M. Cvetič and D. Youm, Entropy of nonextreme charged rotating black holes in string theory, Phys. Rev. D 54 (1996) 2612 [hep-th/9603147] [INSPIRE].
F. Larsen, A String model of black hole microstates, Phys. Rev. D 56 (1997) 1005 [hep-th/9702153] [INSPIRE].
M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Killing Horizons: Negative Temperatures and Entropy Super-Additivity, Phys. Rev. D 98 (2018) 106015 [arXiv:1806.11134] [INSPIRE].
R. Monteiro and J.E. Santos, Negative modes and the thermodynamics of Reissner-Nordstrom black holes, Phys. Rev. D 79 (2009) 064006 [arXiv:0812.1767] [INSPIRE].
R. Monteiro, M.J. Perry and J.E. Santos, Thermodynamic instability of rotating black holes, Phys. Rev. D 80 (2009) 024041 [arXiv:0903.3256] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2009.00015
Rights and permissions
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.
About this article
Cite this article
Ma, L., Li, YZ. & Lü, H. D = 5 rotating black holes in Einstein-Gauss-Bonnet gravity: mass and angular momentum in extremality. J. High Energ. Phys. 2021, 201 (2021). https://doi.org/10.1007/JHEP01(2021)201
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2021)201