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

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 $Ad{S}_4$ 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 $\kappa t_{\ast }=\log \mathcal{S}$ 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.

21-pages, 4-figures

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• Fast Scrambling of mutual information in Kerr-AdS${}_{\text{5}}$
• Localized chaos due to rotating shock waves in Kerr-AdS black holes and their ultraspinning version
• Scrambling in charged hairy black holes and the Kasner interior
• Jackiw-Teitelboim gravity and near-extremal BTZ thermodynamics
• JT gravity and near-extremal thermodynamics for Kerr black holes in $Ad{S}_{4,5}$ for rotating perturbations
• Stationary Solution to Charged Hairy Black Hole in AdS4: Kasner Interior, Rotating Shock Waves, and Fast Scrambling