Chaos in charged AdS black hole extended phase space

TL;DR

This paper analytically investigates chaos in charged AdS black holes within extended phase space, linking chaotic behavior to phase transitions and deriving charge constraints for chaos.

Contribution

First analytical study connecting chaos in black holes with phase transitions using Poincare-Melnikov theory and deriving charge constraints for chaos.

Findings

Chaos occurs in spinodal and small-large black hole regions

A charge constraint necessary for chaos is derived

First to link chaos with black hole phase structure

Abstract

We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare-Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small - large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.