P-V criticality of AdS black holes in a general framework

TL;DR

This paper introduces a universal approach to analyze the critical behavior of AdS black holes, showing that critical exponents are fixed for metrics exhibiting van der Waals-like phase transitions, independent of specific metric details.

Contribution

It presents a novel method based on universal thermodynamic formulas to determine critical exponents without relying on metric-specific phase transition analysis.

Findings

Critical exponents match those of van der Waals systems.

The approach is metric-independent and relies on universal thermodynamic relations.

Critical exponents are fixed for metrics with van der Waals-like phase transitions.

Abstract

In black hole thermodynamics, it has been observed that AdS black holes behave as van der Waals system if one interprets the cosmological constant as a pressure term. Also the critical exponents for the phase transition of AdS black holes and the van der Waals systems are same. Till now this type of analysis is done by two steps. In the first step one shows that a particular metric allows phase transition and in the second step, using this information, one calculates the exponents. Here, we present a different approach based on two universal inputs (the general forms of the Smarr formula and the first law of thermodynamics) and one assumption regarding the existence of van der Waal like critical point for a metric. We find that the same values of the critical exponents can be obtained by this approach. Thus we demonstrate that, though the existence of van der Waal like phase transition depends on specific metrics, the values of critical exponents are then fixed for that set of metrics.