Deforming charged black holes with dipolar differential rotation boundary
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Regular Article - Theoretical Physics
Deforming charged black holes with dipolar differential rotation boundary Tong-Tong Hua , Shuo Sunb , Hong-Bo Lic , Yong-Qiang Wangd Research Center of Gravitation, Institute of Theoretical Physics, Key Laboratory for Magnetism and Magnetic of the Ministry of Education, Lanzhou University, Lanzhou 730000, China
Received: 5 December 2019 / Accepted: 15 June 2020 © The Author(s) 2020
Abstract Motivated by the recent studies of the novel asymptotically global AdS4 black hole with deformed horizon, we consider the action of Einstein–Maxwell gravity in AdS spacetime and construct the charged deforming AdS black holes with differential boundary. In contrast to deforming black hole without charge, there exists at least one value of horizon for an arbitrary temperature. The extremum of temperature is determined by charge q and divides the range of temperature into several parts. Moreover, we use an isometric embedding in the three-dimensional space to investigate the horizon geometry. The entropy and quasinormal modes of deforming charged AdS black hole are also studied in this paper. Due to the existence of charge q, the phase diagram of entropy is more complicated. We consider two cases of solutions: (1) fixing the chemical potential μ; (2) changing the value of μ according to the values of horizon radius and charge. In the first case, it is interesting to find there exist two families of black hole solutions with different horizon radii for a fixed temperature, but these two black holes have same horizon geometry and entropy. The second case ensures that deforming charged AdS black hole solutions can reduce to standard RN–AdS black holes.
Contents 1 2 3 4
Introduction . . . . . . . . . . . . . . . Action and numerical method . . . . . . Numerical model . . . . . . . . . . . . . Black hole solutions with fixed value of μ 4.1 Horizon geometry . . . . . . . . . . 4.2 Entropy . . . . . . . . . . . . . . .
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4.3 Stability . . . . . . . . . . . . 5 Black hole solutions with μ = 2q y+ . 6 Conclusions and outlook . . . . . . References . . . . . . . . . . . . . . .
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1 Introduction In classical general relativity, due to the uniqueness theorem of black holes [1–4], the asymptotically flat charged black hole solutions with zero angular momentum in four dimensions are named as Reissner–Nordstrom (RN) black holes, which have two spherical event horizons. In four-dimensional anti-de Sitter (AdS) spacetime, it is well-known that except for compact horizons of arbitrary genus, there exist some solutions with noncompact planar or hyperbolic horizons. Because of the development of Anti-de Sitter/conformal field theory (AdS/CFT) correspondence [5–7], it
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