Fast Scrambling of Mutual Information in Kerr-AdS$_4$

TL;DR

This paper investigates how mutual information between two hemispherical regions in a Kerr-AdS4 black hole spacetime is disrupted by shockwaves, revealing bounds on chaos and the effects of angular momentum on scrambling time.

Contribution

It introduces a detailed analysis of mutual information disruption and chaos bounds in Kerr-AdS4, incorporating effects of angular momentum and shockwaves on scrambling dynamics.

Findings

Disruption of mutual information is linked to the lengthening of the HRT surface.

The Lyapunov index is bounded by a modified surface gravity   .

Scrambling time depends on the entropy and angular momentum of the black hole.

Abstract

We compute the disruption of mutual information between the hemispherical subsystems on the left and right CFT$s$ of a Thermofield Double state described by a Kerr geometry in $AdS_4$ due to shockwaves along the equatorial plane. The shockwaves and the subsystems considered respect the axi-symmetry of the geometry. At late times the disruption of the mutual information is given by the lengthening of the HRT surface connecting the two subsystems, we compute the minimum value of the Lyapunov index-$\lambda_L^{(min)}$ at late times and find that it is bounded by $\kappa=\frac{2\pi T_H}{(1-\mu\, \mathcal{L})}$ where $\mu$ is the horizon velocity and $\mathcal{L}$ is the angular momentum per unit energy of the shockwave. At very late times we find the the scrambling time for such a system is governed by $\kappa$ with $\kappa t_*=\log \mathcal{S}$ for large black holes with large entropy $\mathcal{S}$. We also find a term that increases the scrambling time by $\log(1-\mu\,\mathcal{L})^{-1}$ but which does not scale with the entropy of the Kerr geometry.