Chaotic Information Processing by Extremal Black Holes

TL;DR

This paper reviews a regularization scheme for the AdS$_2$/CFT$_1$ correspondence that captures the chaotic and fast quantum computational nature of extremal black holes, aiding in understanding their microstate dynamics.

Contribution

It introduces a regularization method that preserves symmetries and characterizes the unitary evolution of extremal black hole microstates using algebraic number theory techniques.

Findings

Regularization preserves all isometries of bulk and boundary.

Scheme reveals black holes' fast quantum computation capability.

Highlights the chaotic nature of extremal black holes.

Abstract

We review an explicit regularization of the AdS$_2$/CFT$_1$ correspondence, that preserves all isometries of bulk and boundary degrees of freedom. This scheme is useful to characterize the space of the unitary evolution operators that describe the dynamics of the microstates of extremal black holes in four spacetime dimensions. Using techniques from algebraic number theory to evaluate the transition amplitudes, we remark that the regularization scheme expresses the fast quantum computation capability of black holes as well as its chaotic nature.