Thermodynamics, Ruppeiner geometry, and topology of Born-Infeld black hole in asymptotic flat spacetime

Abstract

In the extended phase space, Born-Infeld anti-de Sitter black holes exhibit diverse phase transitions including the van der Waals type and reentrant phase transitions. In this paper, we aim to investigate the potential thermodynamical features for Born-Infeld black holes when the cosmological constant vanishes. Quite differently, although there present the swallow tail behavior of the free energy and temperature-entropy criticality, no phase transition will occur when we consider the thermodynamical stability. Further, based on these findings, the phase structures are explicitly shown with the stable, unstable black hole, and non-black hole regions. After excluding the non-black hole region, we observe that the scalar curvature of the Ruppeiner geometry is always positive, indicating a dominant repulsive interaction for both the stable and unstable black holes. Particularly, we also establish the topology for the thermodynamical critical point. By calculating the topological number, we confirm that this critical point of the Born-Infeld black holes is a conventional one. Although it is not an indicator of the first small-large black hole phase transition, it does signify the emergence of stable intermediate black holes. All these results uncover the thermodynamical features of the Born-Infeld black holes in the absence of the cosmological constant.