A New Phase Transition Related to the Black Hole's Topological Charge

TL;DR

This paper explores a novel phase transition in AdS black holes linked to topological charge, revealing van der Waals-like behavior and critical phenomena through thermodynamic analysis.

Contribution

It introduces the topological charge in black hole thermodynamics and analyzes its associated phase transition, including critical points and coexistence lines, using explicit solutions and free energy methods.

Findings

Identification of divergence in specific heat at critical points

Van der Waals-like T-r and T-S behavior observed

Analytic coexistence lines derived using Maxwell's law

Abstract

The topological charge $\epsilon$ of AdS black hole is introduced in Ref.[1,2], where a complete thermodynamic first law is obtained. In this paper, we investigate a new phase transition related to the topological charge in Einstein-Maxwell theory. Firstly, we derive the explicit solutions corresponding to the divergence of specific heat $C_{\epsilon}$ and determine the phase transition critical point. Secondly, the $T-r$ curve and $T-S$ curve are investigated and they exhibit an interesting van der Waals system's behavior. Critical physical quantities are also obtained which are consistent with those derived from the specific heat analysis. Thirdly, a van der Waals system's swallow tail behavior is observed when $\epsilon>\epsilon_{c}$ in the $F-T$ graph. What's more, the analytic phase transition coexistence lines are obtained by using the Maxwell equal area law and free energy analysis, the results of which are consistent with each other.