Butterfly Velocity Bound and Reverse Isoperimetric Inequality

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 $v_{\mathrm{B}}^2=TS/(2V_{\mathrm{th}}P)$. In doing so, we come upon a near-horizon geometrical formula for the thermodynamical volume $V_{\mathrm{th}}$. 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.

Latex, 25 pages, typos corrected and references added. Further discussion on black hole volume as a quantity in addition to T and S to specify the near-horizon geometry

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Cited by in corpus (2)

• On the Butterfly Effect in 3D Gravity
• Horndeski Gravity and the Violation of Reverse Isoperimetric Inequality