Critical slowing down of black hole phase transition and universal dynamic scaling in AdS black holes

TL;DR

This paper demonstrates that black hole phase transitions in AdS spacetime exhibit universal critical slowing down, with relaxation times following a scaling law near criticality across different black hole types.

Contribution

It extends stochastic dynamics to Kerr AdS black holes and uncovers universal scaling laws for relaxation times near critical points.

Findings

Critical slowing down observed near black hole phase transitions.

Relaxation time scales as |psilon|^{-2/3} near criticality.

Universal dynamical behavior across different black hole systems.

Abstract

We investigate the dynamical critical behaviour of black hole phase transitions in anti de Sitter spacetime by extending the stochastic framework of free energy landscape dynamics to Kerr AdS black holes. By analyzing the Langevin evolution of the entropy (in contrast to the horizon radius in the RN-AdS case) near criticality, we demonstrate that the system exhibits pronounced critical slowing down, characterized by a significant increase of the autocorrelation time as the critical point is approached. This behaviour is further confirmed by the lowest eigenvalue of the Fokker-Planck equation. By analysing the dynamics along different thermodynamic paths, including variations in temperature, pressure, and angular momentum, and considering both directions - towards and away from criticality, we find that the relaxation time obeys a robust scaling relation, $\tau=|\epsilon|^{-2/3}$ near criticality. The same scaling exponent is obtained for RN-AdS, Kerr-AdS, and Bardeen black holes, suggesting the existence of an underlying universal dynamical behaviour across distinct black hole systems. Our results establish a connection between the geometry of the free energy landscape, stochastic nonequilibrium dynamics, and universal critical phenomena in black hole thermodynamics.