Topological properties of black holes in five-dimensional gauged supergravity

TL;DR

This paper investigates the topological characteristics of five-dimensional charged rotating black holes in gauged supergravity, revealing how ensemble conditions and rotational parameters influence their topological numbers and phase transitions.

Contribution

It introduces a detailed analysis of black hole topological numbers in different ensembles and explores how rotational parameters affect supersymmetry and phase transitions.

Findings

Topological numbers are 1 in general, 0 when charge and cosmological constant vanish.

Phase transition depends on pressure and ensemble, occurring under specific conditions.

Rotational parameters influence supersymmetry and the occurrence of phase transitions.

Abstract

In this paper, we study the topological properties of five-dimensional rotating charged black holes in different ensembles.The topological numbers for the black holes are gotten in the grand canonical and canonical ensembles, which are 1. When the charge and cosmological constant disappear, their topological numbers are 0. When the pressure is lower than the critical pressure, the phase transition exists in the canonical ensemble. However, the phase transition also exists in the grand canonical ensemble when the pressure is higher than the critical pressure and two independent rotational parameters are $a=1$ and $b=-1$. This may be due to the fact that the values of the rotational parameters change the supersymmetry of the black hole and lead to the phase transition.