Hawking-Page phase transition of the Schwarzschild AdS black hole with the effective Tolman temperature

TL;DR

This paper investigates the stability and phase transitions of Schwarzschild AdS black holes using an alternative local temperature definition based on the stress tensor, revealing multiple critical temperatures and types of phase transitions.

Contribution

It introduces a new local temperature approach satisfying the Hartle-Hawking vacuum condition, affecting stability analysis and phase transition characterization of Schwarzschild AdS black holes.

Findings

Medium-sized black holes are stable below a critical AdS radius.

Multiple critical temperatures for different phase transitions are identified.

The medium-sized black hole experiences both Hawking-Page and zeroth-order phase transitions.

Abstract

A sufficiently large Schwarzschild AdS black hole with the Hawking temperature has a positive heat capacity and undergoes the Hawking-Page phase transition. Even though an arbitrary isothermal surface of a cavity is introduced, the essential features about the stability and phase transition of the Schwarzschild AdS black hole remain the same. In this paper, we study the stability and the Hawking-Page phase transition of the Schwarzschild AdS black hole by employing an alternative local temperature satisfying the Hartle-Hawking vacuum condition which states that the ingoing and outgoing fluxes vanish at the horizon so that the local temperature is naturally zero there. The different definition of the local temperature based on the stress tensor approach provides different types of stability and phase transition. For a AdS curvature radius below a critical one, the medium-sized black hole is found to be stable and the other small and large black holes turn out to be unstable regardless of the AdS curvature radius. Furthermore, we encounter various critical temperatures. The first one is for the Hawking-Page phase transition between the medium-sized black hole and thermal AdS, and the second one is for a phase transition between the large black hole and thermal AdS; however, the latter one is not essential because the large black hole and thermal AdS eventually collapse to the medium-sized black hole. Interestingly, we find an additional critical temperature related to the zeroth-order phase transition between the medium-sized black hole and thermal AdS. Consequently, the medium-sized black hole undergoes both the Hawking-Page phase transition and the zeroth-order phase transition.