Coexistence curves and molecule number densities of AdS black holes in the reduced parameter space

TL;DR

This paper analyzes the coexistence curves and molecule number densities of various AdS black holes in a reduced parameter space, revealing universal behaviors and differences linked to their underlying equations of state.

Contribution

It derives universal analytic expressions for coexistence curves and molecule densities of AdS black holes, highlighting their similarities and differences across theories.

Findings

Coexistence curves are universal and theory-independent.

Molecule density differences match RN-AdS black holes for certain cases.

Gauss-Bonnet AdS black holes show distinct molecule density behavior.

Abstract

In this paper, we investigate the coexistence curves and molecule number densities of $f(R)$ AdS black holes and Gauss-Bonnet AdS black holes. Specifically, we work with the reduced parameter space and derive the analytic expressions of the universal coexistence curves that are independent of theory parameters. Moreover, we obtain the explicit expressions of the physical quantity describing the difference of the number densities of black hole molecules between the small and large black hole. It is found that both the coexistence curve and the difference of the molecule number densities of $f(R)$ AdS black holes coincide with those of RN-AdS black holes. It may be attributed to the same equation of state they share in the reduced parameter space. The difference of the molecule number densities between the small and large Gauss-Bonnet AdS black hole exhibits different behavior. This may be attributed to the fact that the charge of RN-AdS black hole is non-trivial. Our research will not only deepen the understanding of both the physics along the coexistence curve and the underlying microscopic freedom of AdS black holes, but also highlight the importance of the law of corresponding states.