Temporal and Spatial Chaos of RN-AdS Black Holes Immersed in Perfect Fluid Dark Matter

TL;DR

This paper explores the complex chaotic behavior of Reissner-Nordström Anti-de Sitter black holes immersed in perfect fluid dark matter, analyzing both temporal and spatial chaos through dynamical equations and the Melnikov method.

Contribution

It introduces a novel analysis of chaos in RN-AdS black holes within dark matter environments, highlighting the effects of charge, temperature, and phase transition conditions.

Findings

Existence of a critical amplitude influencing temporal chaos.

Black hole charge and state parameter affect the critical amplitude.

Spatial chaos persists regardless of perturbation intensity.

Abstract

We investigate the thermodynamic chaos of RN-AdS black holes immersed in Perfect Fluid Dark Matter by considering the dynamical equations of the fluid system evolved in the spinodal region. Based on the Melnikov method, it is shown that there exists a critical amplitude that affects the temporal chaos. And the influence of black holes charge and state parameter on the critical amplitude is investigated with specific initial temperature. Then, for inevitable spatial chaos, three different types of portraits are discssued according to the difference between the phase transition pressure and the ambient pressure. Additionally, we check the local equilibrium near saddle points which shows that spatial chaos always exists regardless of the perturbation intensity.