# Reduced thermodynamics and an exact phase transition of five-dimensional Kerr-AdS black holes with equal spin parameters

## TL;DR

This paper investigates the phase transitions and critical phenomena of five-dimensional Kerr-AdS black holes with equal spins, revealing unique thermodynamic behaviors and providing precise coexistence curves and critical exponents.

## Contribution

It presents the exact phase structure, reduced thermodynamic laws, and critical exponents for five-dimensional multi-spinning Kerr-AdS black holes, including unequal spins.

## Key findings

- Distinct thermodynamic laws in reduced parameter space
- Accurate coexistence curve fitting formula
- Numerical analysis of critical points for unequal spins

## Abstract

Multi-spinning higher dimensional Kerr-AdS black holes admit the stable small-large black hole phase transition of van der Waals type. In this paper, we study the exact critical phenomena and phase structure in five-dimensional spacetime. First, we examine the thermodynamic laws in the reduced parameter space and find that they are quite different from the conventional thermodynamic laws. Then based on the reduced laws, the phase structure in different parameter spaces is investigated. The stable and metastable black hole phases are clearly displayed. We present a highly accurate fitting formula for the coexistence curve of small and large black hole phases. Using this fitting formula, we examine the critical exponents when the black hole system approaches the critical point along the coexistence curve. Moreover, employing the dimensional analysis and symmetry analysis, we also give a numerical study of the critical point for the unequal spinning black holes. These results are very useful on further understanding the microstructure of the multi-spinning black holes in higher dimensional spacetime.