Butterflies with rotation and charge

TL;DR

This paper investigates how small perturbations affect the dynamics of rotating and charged black holes in 2+1 dimensions, revealing exponential growth in effects related to the butterfly effect without explicit dependence on charge or rotation.

Contribution

It analyzes the butterfly effect in rotating and charged black holes using shock wave perturbations and explores implications for correlation functions in these spacetimes.

Findings

Perturbation effects grow exponentially with a rate set by temperature.

Rotation and charge do not explicitly influence the growth rate.

The study discusses challenges in extending results to higher-dimensional black holes.

Abstract

We explore the butterfly effect for black holes with rotation or charge. We perturb rotating BTZ and charged black holes in 2+1 dimensions by adding a small perturbation on one asymptotic region, described by a shock wave in the spacetime, and explore the effect of this shock wave on the length of geodesics through the wormhole and hence on correlation functions. We find the effect of the perturbation grows exponentially at a rate controlled by the temperature; dependence on the angular momentum or charge does not appear explicitly. We comment on issues affecting the extension to higher-dimensional charged black holes.