Topology of black hole thermodynamics: A brief review

TL;DR

This review summarizes recent progress in understanding black hole thermodynamics through topological methods, classifying systems into universality classes and analyzing their physical implications.

Contribution

It provides a comprehensive overview of topological frameworks and calculations of topological numbers in various black hole thermodynamic phenomena.

Findings

Black hole systems can be categorized into universality classes using topological numbers.

Topological numbers are calculated for solutions, critical points, and phase transitions.

The research offers insights into the physical significance of topological classifications.

Abstract

Recent explorations of topological aspects in black hole thermodynamics have achieved unprecedented progress. By utilizing topological numbers, different black hole systems can be categorized into distinct universality classes. This universal classification is particularly evident in thermodynamic limits, offering valuable insights for developing a comprehensive quantum gravity framework. This review highlights the latest advancements in this field. Specifically, we outline fundamental topological frameworks underlying black hole solutions, critical points, Davies points, and the Hawking-Page phase transition. For each scenario, we calculate the associated topological numbers and analyze their physical significance. Furthermore, we explore the practical implications arising from this research.