Stationary Solution to Charged Hairy Black Hole in AdS4: Kasner Interior, Rotating Shock Waves, and Fast Scrambling

TL;DR

This paper studies charged hairy black holes in AdS4, analyzing their interior Kasner geometry, effects of rotating shock waves on wormhole connectivity, and how charge and rotation influence chaos and scrambling times.

Contribution

It introduces a detailed holographic analysis of charged hairy black holes with shock waves, revealing how charge and rotation affect chaos and information scrambling.

Findings

Shock waves lengthen the wormhole and disrupt correlations.

Scrambling time depends logarithmically on black hole entropy.

Charge and rotation modulate Lyapunov exponent and scrambling delay.

Abstract

We consider a stationary solution of a charged black hole with scalar hair in AdS$_4$, where the scalar field is coupled to a $U(1)$ Maxwell gauge field. Near the singularity, the spacetime transitions into a more general Kasner geometry. The black hole is then injected with rotating and charged gravitational shock waves in the Dray-'t Hooft solution. These shock waves lengthen the wormhole connecting the two asymptotic boundaries, thereby disrupting the correlations between them. The correlation, quantified by the quantum mutual information between subregions on the left and right boundaries, vanishes at a characteristic timescale known as the scrambling time, which depends logarithmically on the black hole entropy. The mutual information is computed holographically using the Ryu-Takayanagi prescription for entanglement entropy. We investigate how the rotation and charge of both the black hole and the shock waves affect chaotic properties such as the scrambling time delay and the Lyapunov exponent. The interaction between the charges of the black hole and the shock waves introduces a delay in the scrambling process. We find that as the strength of the boundary deformation increases, both the Lyapunov exponent and the scrambling time delay decrease monotonically. Furthermore, the angular momentum of the shock waves enhances both the Lyapunov exponent and the scrambling time delay.