Mutual correlation in the shock wave geometry

TL;DR

This paper investigates how mutual correlation behaves in shock wave geometries of Reissner Nordström AdS black holes, revealing how charge and horizon shifts influence boundary correlations in static and dynamic settings.

Contribution

It introduces a detailed analysis of mutual correlation in shock wave geometries, highlighting the effects of charge and horizon shifts on boundary correlations in AdS black holes.

Findings

Mutual correlation exists for large enough boundary regions in static backgrounds.

Higher charge reduces mutual correlation in static backgrounds.

Horizon shifts decrease mutual correlation in dynamic shock wave geometries.

Abstract

We probe the shock wave geometry with the mutual correlation in a spherically symmetric Reissner Nordstr\"om AdS black hole on the basis of the gauge/gravity duality. In the static background, we find that the regions living on the boundary of the AdS black holes are correlated provided the considered regions on the boundary are large enough. We also investigate the effect of the charge on the mutual correlation and find that the bigger the value of the charge is, the smaller the value of the mutual correlation will to be. As a small perturbation is added at the AdS boundary, the horizon shifts and a dynamical shock wave geometry forms after long time enough. In this dynamic background, we find that the greater the shift of the horizon is, the smaller the mutual correlation will to be. Especially for the case that the shift is large enough, the mutual correlation vanishes, which implies that the considered regions on the boundary are uncorrelated. The effect of the charge on the mutual correlation in this dynamic background is found to be the same as that in the static background.