Deforming black holes with odd multipolar differential rotation boundary

Abstract

Motivated by the novel asymptotically global AdS${}_4$ solutions with deforming horizon in [JHEP {\bf 1802}, 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 $\epsilon$, below which the stable large black hole solutions could exist, are not a constant for $T>T_{schw}=\sqrt{3}/2\pi \simeq 0.2757$. When temperature is much higher than $T_{schw}$, even though the norm of Killing vector ${\partial }_t$ keeps timelike for some regions of $\epsilon <2$, 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 ${\partial }_t$ for some regions of $\epsilon >2$, 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 $\epsilon$. 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.

arXiv comment19 pages, 11 figures. arXiv admin note: text overlap with arXiv:1903.11967

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Cited by in corpus (1)

• Deforming charged black holes with dipolar differential rotation boundary