Abstract
We study all transverse deformations of the extremal Reissner-Nordström–(A)dS horizon in the Einstein-Maxwell theory. No symmetry assumptions are needed. It is shown, that for the generic values of a charge, the only allowed deformation is spherically symmetric. However, it is shown that for fine-tuned values of the charge, the space of deformations is larger, yet still finite-dimensional.
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References
W. Israel, Event horizons in static vacuum space-times, Phys. Rev. 164 (1967) 1776 [INSPIRE].
S.W. Hawking, Black holes in general relativity, Commun. Math. Phys. 25 (1972) 152 [INSPIRE].
B. Carter, Axisymmetric black hole has only two degrees of freedom, Phys. Rev. Lett. 26 (1971) 331 [INSPIRE].
D.C. Robinson, Uniqueness of the Kerr black hole, Phys. Rev. Lett. 34 (1975) 905 [INSPIRE].
P.O. Mazur, Proof of uniqueness of the Kerr-Newman black hole solution, J. Phys. A 15 (1982) 3173 [INSPIRE].
P.T. Chrusciel and R.M. Wald, On the topology of stationary black holes, Class. Quant. Grav. 11 (1994) L147 [gr-qc/9410004] [INSPIRE].
T.M. Adamo, C.N. Kozameh and E.T. Newman, Null geodesic congruences, asymptotically flat space-times and their physical interpretation, Living Rev. Rel. 12 (2009) 6 [arXiv:0906.2155] [INSPIRE].
C.A.R. Herdeiro and E. Radu, Static Einstein-Maxwell black holes with no spatial isometries in AdS space, Phys. Rev. Lett. 117 (2016) 221102 [arXiv:1606.02302] [INSPIRE].
H.K. Kunduri and J. Lucietti, Uniqueness of near-horizon geometries of rotating extremal AdS4 black holes, Class. Quant. Grav. 26 (2009) 055019 [arXiv:0812.1576] [INSPIRE].
D. Dobkowski-Rylko, W. Kamiński, J. Lewandowski and A. Szereszewski, The Near Horizon Geometry equation on compact 2-manifolds including the general solution for g > 0, Phys. Lett. B 785 (2018) 381 [arXiv:1807.05934] [INSPIRE].
J. Lewandowski and T. Pawlowski, Extremal isolated horizons: a Local uniqueness theorem, Class. Quant. Grav. 20 (2003) 587 [gr-qc/0208032] [INSPIRE].
J. Lewandowski and T. Pawlowski, Quasi-local rotating black holes in higher dimension: geometry, Class. Quant. Grav. 22 (2005) 1573 [gr-qc/0410146] [INSPIRE].
H.K. Kunduri and J. Lucietti, Classification of near-horizon geometries of extremal black holes, Living Rev. Rel. 16 (2013) 8 [arXiv:1306.2517] [INSPIRE].
C. Li and J. Lucietti, Transverse deformations of extreme horizons, Class. Quant. Grav. 33 (2016) 075015 [arXiv:1509.03469] [INSPIRE].
A. Fontanella and J.B. Gutowski, Moduli spaces of transverse deformations of near-horizon geometries, J. Phys. A 50 (2017) 215202 [arXiv:1610.09949] [INSPIRE].
C. Li and J. Lucietti, Electrovacuum spacetime near an extreme horizon, Adv. Theor. Math. Phys. 23 (2019) 1903 [arXiv:1809.08164] [INSPIRE].
M. Kolanowski, J. Lewandowski and A. Szereszewski, Extremal horizons stationary to the second order: new constraints, Phys. Rev. D 100 (2019) 104057 [arXiv:1907.00955] [INSPIRE].
D. Kastor and J.H. Traschen, Cosmological multi-black hole solutions, Phys. Rev. D 47 (1993) 5370 [hep-th/9212035] [INSPIRE].
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Kolanowski, M. Towards the black hole uniqueness: transverse deformations of the extremal Reissner-Nordström-(A)dS horizon. J. High Energ. Phys. 2022, 42 (2022). https://doi.org/10.1007/JHEP01(2022)042
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DOI: https://doi.org/10.1007/JHEP01(2022)042