Phase-space Path Integral Approach to the Kinetics of Black Hole Phase Transition in Massive Gravity

TL;DR

This paper models black hole phase transitions in massive gravity using a phase-space path integral approach, analyzing stability and transition paths influenced by charge and graviton mass.

Contribution

It introduces a stochastic dynamical framework combining free energy landscapes and path integrals to study black hole phase transitions in massive gravity.

Findings

Identifies stable and unstable black hole phases.

Analyzes the impact of charge and graviton mass on phase transition behavior.

Determines dominant kinetic paths between phases.

Abstract

The dynamics of the state-switching process of black holes in dRGT massive gravity theory is presented using free energy landscape and stochastic Langevin equations. The free energy landscape is constructed using the Gibbons-Hawking path integral method. The black hole phases are characterized by taking its horizon radius as the order parameter. The free energy landscape provides three black hole phases: small, intermediate, and large. The small and large black holes are thermodynamically stable whereas the intermediate one is unstable. The Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) functional describes the stochastic dynamics of black hole phase transition. The Hamiltonian flow lines are obtained from the MSRJD functional and are used to analyze the stability and the phase transition properties. The dominant kinetic path between different phases is discussed for various configurations of the free energy landscape. We discuss the effect of black hole charge and the graviton mass on the critical behavior of black hole phase transition.