Holographic Butterfly Velocities in Brane Geometry and Einstein-Gauss-Bonnet Gravity with Matters

TL;DR

This paper extends the butterfly velocity formula to anisotropic spacetimes, applies it to various brane backgrounds, and explores its invariance under dimensional reduction, also deriving a general formula for Einstein-Gauss-Bonnet gravity with matter.

Contribution

It generalizes butterfly velocity calculations to anisotropic geometries and Einstein-Gauss-Bonnet gravity with matter, revealing invariance properties and providing a unified formula.

Findings

Butterfly velocities in M-branes match those in fundamental strings.

Butterfly velocity is conjectured to be invariant under double-dimensional reduction.

A general formula for butterfly velocity in Einstein-Gauss-Bonnet gravity with matter is derived.

Abstract

In the first part of the paper we generalize the butterfly velocity formula to anisotropic spacetime. We apply the formula to evaluate the butterfly velocities in M-branes, D-branes and strings backgrounds. We show that the butterfly velocities in M2-branes, M5-branes and the intersection M2$\bot$M5 equal to those in fundamental strings, D4-branes and the intersection F1$\bot$D4 backgrounds, respectively. These observations lead us to conjecture that the butterfly velocity is generally invariant under a double-dimensional reduction. In the second part of the paper, we study the butterfly velocity for Einstein-Gauss-Bonnet gravity with arbitrary matter fields. A general formula is obtained. We use this formula to compute the butterfly velocities in different backgrounds and discuss the associated properties.