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

Understand

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.