On the Dynamics of Near-Extremal Black Holes

Abstract

We analyse the dynamics of near-extremal Reissner-Nordström black holes in asymptotically four-dimensional Anti-de Sitter space (AdS${}_4$). We work in the spherically symmetric approximation and study the thermodynamics and the response to a probe scalar field. We find that the behaviour of the system, at low energies and to leading order in our approximations, is well described by the Jackiw-Teitelboim (JT) model of gravity. In fact, this behaviour can be understood from symmetry considerations and arises due to the breaking of time reparametrisation invariance. The JT model has been analysed in considerable detail recently and related to the behaviour of the SYK model. Our results indicate that features in these models which arise from symmetry considerations alone are more general and present quite universally in near-extremal black holes.

arXiv comment44 (=26+18) pages, 1 figure, 6 appendices; v2: references added; v3: minor changes made; v4: additional references added, version accepted in JHEP

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