Butterfly Velocity Bound and Reverse Isoperimetric Inequality

Understand

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.