Abstract
Extremal black holes have vanishing Hawking temperatures. In this article, we argue that for asymptotically AdS black holes, at extremality, a particular class of correlators in the dual CFT can exhibit exponential, maximally chaotic growth with a non-vanishing temperature. Our approach, at extremality, is two-fold. First, we geometrically investigate the modes that are responsible for chaos. Secondly, we study the dynamics of a probe string to capture chaos in worldsheet correlators. For rotating BTZ at extremality, the corresponding Lyapunov exponent is determined by the left-moving temperature. In higher dimensional AdS-Kerr geometries, on the other hand, the corresponding Lyapunov exponent becomes a non-trivial function of the Frolov-Thorne temperatures.
Highlights
The study of black holes via holography has allowed us uncover interesting features of quantum gravity, especially in anti–de Sitter (AdS) spacetimes
We have analyzed the case of extremal chaos by studying the near horizon or the throat region of extremal and near extremal BTZ
We find that in the near horizon region, the JT model captures the contribution of what we term as thermal modes toward chaos—these account for the λL 1⁄4 2π=β < λ−L and only
Summary
The study of black holes via holography has allowed us uncover interesting features of quantum gravity, especially in anti–de Sitter (AdS) spacetimes. This would be useful in higher dimensions as holographic analysis of computing the Lyapunov exponent using known techniques in literature would be a cumbersome task in rotating black hole geometries in dimensions >3. RN black holes are not charged under spacetime symmetries like the Kerr or BTZ but an internal Uð1Þ symmetry In this regard, their near horizon effective gravity theory may seem to be holographically dual to charged SYK models which have been thoroughly investigated and do not seem to possess extremal chaos, i.e., Lyapunov index is zero at the zero temperature IR limit.
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