Temporal and spatial chaos in the Kerr-AdS black hole in an extended phase space

TL;DR

This paper investigates chaos in Kerr-AdS black holes within extended phase space, revealing conditions under which temporal and spatial chaos occur due to perturbations, with implications for black hole thermodynamics.

Contribution

It introduces a Melnikov method analysis of chaos in Kerr-AdS black holes under temporal and spatial perturbations, highlighting the conditions for chaos onset.

Findings

Temporal chaos occurs only above a critical perturbation amplitude.

Spatial chaos always occurs regardless of perturbation amplitude.

Chaos is linked to the black hole's angular momentum.

Abstract

Based on the Melnikov method, we investigate chaotic behaviors in the extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole under temporal and spatial perturbations. Our results show that the temporal perturbation coming from a thermal quench of the spinodal region in the phase diagram may cause the temporal chaos only when the perturbation amplitude is above a critical value, which involves the angular momentum . Under the spatial perturbation, however, it is found that the spatial chaos always occurs, which is independent of the perturbation amplitude.