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

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.

arXiv comment22 pages, 14 figures

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Cited by in corpus (7)

• Delocalizing Entanglement of Anisotropic Black Branes
• Influence of inhomogeneities on holographic mutual information and butterfly effect
• Butterfly Velocity Bound and Reverse Isoperimetric Inequality
• Chaos, Diffusivity, and Spreading of Entanglement in Magnetic Branes, and the Strengthening of the Internal Interaction
• Shock waves, black hole interiors and holographic RG flows
• Holographic Butterfly Velocities in Brane Geometry and Einstein-Gauss-Bonnet Gravity with Matters
• Butterfly Velocity in Quadratic Gravity