Evidence that the Rate of Evolution of a Black Hole Interior Has a Holographic Dual

Understand

A ``large'' AdS black hole can attain equilibrium with its own Hawking radiation, and in that condition it is thought to be dual to a strongly coupled field theory, also at equilibrium.

• But the interior of the black hole is by no means static: the geometry of spatial sections lying inside the event horizon evolves at some rate.
• This prompts the obvious question: can this rate possibly have a holographic dual? We present circumstantial evidence that such a dual does exist.
• We do this by making concrete proposals for two objects: first, a rough measure (already suggested in the literature) of the rate at which the unitary evolution of the state vector describing equilibrated strongly coupled matter evolves; and, second, a rough measure of the rate at which the interior (just under the horizon) evolves (in the case of the AdS$_5$-Kerr black hole).