Deforming black holes with odd multipolar differential rotation boundary

Abstract

Motivated by the novel asymptotically global AdS 4 solutions with deforming horizon in [JHEP 1802[JHEP , 060 (2018], we analyze the boundary metric with odd multipolar differential rotation and numerically construct a family of deforming solutions with tripolar differential rotation boundary, including two classes of solutions: solitons and black holes. We find that the maximal values of the rotation parameter ε, below which the stable large black hole solutions could exist, are not a constant for T > T schw = √ 3/2π 0.2757. When temperature is much higher than T schw , even though the norm of Killing vector ∂ t keeps timelike for some regions of ε < 2, solitons and black holes with tripolar differential rotation could be unstable and develop hair due to superradiance. As the temperature T drops toward T schw , we find that though there exists the spacelike Killing vector ∂ t for some regions of ε > 2, solitons and black holes still exist and do not develop hair due to superradiance. Moreover, for T T schw , the curves of entropy firstly combine into one curve and then separate into two curves again, in the case of each curve there are two solutions at a fixed value of ε. In addition, we study the deformations of horizon for black holes by using an isometric embedding in the hyperbolic three-dimensional space. Furthermore, we also study the quasinormal modes of the solitons and black holes, which have analogous behaviours to that of dipolar rotation and quadrupolar rotation. *

Deforming charged black holes with dipolar differential rotation boundary

“…Because of superradiance, both solitons and black holes develop hair at ε > 2. Motivated by this work, we also studied deforming solutions with odd multipolar [17] and even multipolar [18] differential rotation boundary. Furthermore, the authors in [19] numerically studied a class of vacuum solutions with a noncompact, differential rotation boundary metric.…”

“…Until now, the works of deforming AdS black hole with differential boundary [15,17,18] were only studied in the cases without charge. It would be interesting to see whether there exist the charged deforming AdS black hole solutions in Einstein-Maxwell-AdS spacetime.…”