Butterfly Effect and Holographic Mutual Information under External Field and Spatial Noncommutativity

TL;DR

This paper investigates how external magnetic, electric fields, and spatial noncommutativity influence the butterfly effect and holographic mutual information in black brane spacetimes, finding they do not alter scrambling time but enhance mutual information.

Contribution

It extends previous models to include external fields and noncommutativity, analyzing their effects on information scrambling and mutual information in holographic setups.

Findings

External fields do not modify the scrambling time.

External fields and noncommutativity enhance mutual information.

Backreaction effects on mutual information are studied in three models.

Abstract

We apply the transformation of mixing azimuthal and internal coordinate or mixing time and internal coordinate to a stack of N black M-branes to find the Melvin spacetime of a stack of N black D-branes with magnetic or electric flux in string theory, after the Kaluza-Klein reduction. We slightly extend previous formulas to investigate the external magnetic and electric effects on the butterfly effect and holographic mutual information. It shows that the Melvin fields do not modify the scrambling time and will enhance the mutual information. In addition, we also T-dualize and twist a stack of N black D-branes to find a Melvin Universe supported by the flux of the NSNS b-field, which describes a non-comutative spacetime. It also shows that the spatial noncommutativity does not modify the scrambling time and will enhance the mutual information. We also study the corrected mutual information in the backreaction geometry due to the shock wave in our three model spacetimes.