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arXiv · 1701.05204

Butterfly Velocity Bound and Reverse Isoperimetric Inequality

Xing-Hui Feng·H. Lu
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Abstract

We study the butterfly effect of the AdS planar black holes in the framework of Einstein's general relativity. We find that the butterfly velocities can be expressed by a universal formula $v_{\rm B}^2 = TS/(2V_{\rm th} P)$. In doing so, we come upon a near-horizon geometrical formula for the thermodynamical volume $V_{\rm th}$. We verify the volume formula by examining a variety of AdS black holes. We also show that the volume formula implies that the conjectured reverse isoperimetric inequality follows straightforwardly from the null-energy condition, for static AdS black holes. The inequality is thus related to an upper bound of the butterfly velocities.

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Xing-Hui Feng, H. Lu. 2017-01-18. Butterfly Velocity Bound and Reverse Isoperimetric Inequality. https://doi.org/10.1103/physrevd.95.066001

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