Phase transition and critical phenomena of black holes: A general approach

TL;DR

This paper introduces a universal framework for analyzing black hole phase transitions, deriving critical exponents and scaling laws without relying on specific black hole solutions, revealing their universal nature across different spacetimes.

Contribution

It provides a general, solution-independent method to determine critical phenomena in black hole thermodynamics, simplifying previous case-by-case analyses.

Findings

Critical exponents are universal across black hole types.

Most scaling powers are independent of spacetime dimensions.

The framework matches results from explicit black hole solutions.

Abstract

We present a general framework to study the phase transition of a black hole. Assuming that there is a phase transition, it is shown that without invoking any specific black hole, the critical exponents and the scaling powers can be obtained. We find that the values are exactly same which were calculated by taking explicit forms of different black hole spacetimes. The reason for this universality is also explained. The implication of the analysis is -- one does not need to investigate this problem case by case, what the people are doing right now. We also observe that these, except two such quantities, are independent of the details of the spacetime dimensions.