Phase Transition and Critical Behavior in Gravitational Collapse

TL;DR

This paper analyzes gravitational collapse using thermodynamic concepts, identifying a phase transition characterized by a critical condition that links geometric stability with thermodynamic criticality, and highlights the apparent horizon as a universal critical surface.

Contribution

It introduces a thermodynamic framework for gravitational collapse and establishes a universal critical condition for phase transition independent of geometry type.

Findings

Critical condition $ ext{d}\kappa_{hk}/ ext{d}t=0$ signifies second order phase transition.

The phase transition condition is geometry-independent.

Apparent horizon acts as a universal critical surface in collapse phase-space.

Abstract

We present a thermodynamic analysis of spherically symmetric gravitational collapse. Using the Hayward-Kodama formalism, we treat a collapsing sphere as a thermodynamic system and express the surface gravity $\kappa_{hk}$ in terms of the geometric variables. We derive the specific heat capacities and identify a critical condition $\dot{\kappa}_{hk} = 0$ as the locus of second order phase transition during the collapse. Through specific examples, we demonstrate that the condition is independent of singular/non-singular nature of the geometry. We also find that the critical condition of phase transition is equivalent to a stationary condition of the expansion of null congruence. This establishes a direct correspondence between geometric stability and thermodynamic criticality, allowing the identification of apparent horizon as a universal critical surface in the phase-space of gravitational collapse.