Disrupting Entanglement of Black Holes

TL;DR

This paper investigates how entanglement between regions in strongly coupled CFTs, modeled by charged black holes in AdS, is affected by perturbations, revealing a universal timescale for disruption.

Contribution

It introduces a detailed analysis of mutual information transition scales and generalizes the butterfly effect to charged black holes, proposing a universal disruption timescale.

Findings

Mutual information vanishes for small regions and is positive for large ones.

Critical length scale diverges for extremal black holes.

Disruption of mutual information occurs after a logarithmic timescale in energy perturbations.

Abstract

We study entanglement in thermofield double states of strongly coupled CFTs by analyzing two-sided Reissner-Nordstrom solutions in AdS. The central object of study is the mutual information between a pair of regions, one on each asymptotic boundary of the black hole. For large regions the mutual information is positive and for small ones it vanishes; we compute the critical length scale, which goes to infinity for extremal black holes, of the transition. We also generalize the butterfly effect of Shenker and Stanford to a wide class of charged black holes, showing that mutual information is disrupted upon perturbing the system and waiting for a time of order $\log E/\delta E$ in units of the temperature. We conjecture that the parametric form of this timescale is universal.