# Chaos in Born-Infeld-AdS black hole within extended phase space

## TL;DR

This paper investigates chaotic dynamics in Born-Infeld-AdS black holes under thermal perturbations, revealing conditions for chaos onset depending on black hole parameters and perturbation characteristics.

## Contribution

It introduces the analysis of chaos in Born-Infeld-AdS black holes using Melnikov method, highlighting how parameters influence chaos onset.

## Key findings

- Chaos occurs when perturbation amplitude exceeds a critical value
- Larger Born-Infeld parameter or charge facilitates chaos onset
- Space-periodic perturbations always induce chaos regardless of amplitude

## Abstract

Born-Infeld-AdS black holes in extended phase space may possess phase structures resembling that of van der Waals fluid in four-dimensional spacetime. We study dynamics of its state, which is in the unstable spinodal region initially on phase space, under time-periodic thermal perturbations. By applying the Melnikov method, it is found that there exists a critical amplitude $\gamma_c$ of the perturbations, which depends on the Born-Infeld parameter $b$ and the black hole charge $Q$, such that chaos occurs for $\gamma > \gamma_c$. We found that larger $b$ or $Q$ makes the onset of chaos easier. Space-periodic thermal perturbations on its equilibrium state are also studied and there is always chaos for whatever the perturbation amplitude is.