Phase transition structure and breaking of universal nature of central charge criticality in a Born-Infeld $AdS$ black hole

TL;DR

This paper investigates how the non-linear Born-Infeld parameter affects the thermodynamics and critical behavior of AdS black holes, revealing the breakdown of previously observed universal critical central charge and new phase transition phenomena.

Contribution

It extends the study of critical behavior in black hole thermodynamics to Born-Infeld AdS black holes, showing the non-linearity breaks the universality of the critical central charge.

Findings

Universal critical central charge breaks down with Born-Infeld non-linearity.

Existence of a temperature threshold below which no black holes form for small Born-Infeld parameter.

Modified thermodynamic volume and chemical potential due to Born-Infeld effects.

Abstract

In this paper we have considered the thermodynamics of a Born-Infeld $AdS$ black hole using inputs from the dual boundary field theory. Here, we have varied the cosmological constant $\Lambda$ and the Newton's gravitational constant $G$ along with the Born-Infeld parameter $b$ in the bulk. A novel universal critical behaviour of the central charge (occurring in the boundary conformal field theory) in extended black hole thermodynamics for charged black holes has been recently observed \cite{mann1}, and we have extended this study to Born-Infeld $AdS$ black holes. The Born-Infeld parameter has the dimension of inverse length, therefore, when considered in the first law of thermodynamics of the bulk in the mixed form which includes the central charge of the boundary conformal field theory, it modifies the thermodynamic volume and the chemical potential (which are conjugate to pressure and central charge respectively). We observe that due to this inclusion of the Born-Infeld non-linearity in this analysis, the universal nature of the critical value of the central charge observed in \cite{mann1} breaks down. We also observe an interesting behaviour of the free energy of the black hole with Hawking temperature due to the variations in both the central charge and the Born-Infeld parameter. It is also observed in our analysis that for a sufficiently small value of the Born-Infeld parameter (small value of this parameter has more prominent non-linear effects), there exists a critical value of the temperature below which no black hole can exist.