Extended thermodynamical topology of black hole

TL;DR

This paper introduces a unified framework called extended thermodynamical topology that classifies black hole phases and critical phenomena using topological invariants, applicable to Einstein and Lovelock gravity.

Contribution

It develops a comprehensive approach integrating multiple topological invariants to analyze black hole thermodynamics and applies it to higher-dimensional gravity models.

Findings

Unified topological framework for black hole thermodynamics

Application to Einstein and Lovelock gravity models

Connection between critical exponents and topological invariants

Abstract

Thermodynamical topology has emerged as a powerful framework for classifying the thermodynamical behavior of black holes. Three distinct yet complementary topological invariants have been employed to characterize black hole phases, spinodal curves, and critical points in black hole thermodynamics. In this work, we develop a unified framework that integrates these three topological approaches and introduce the concept of extended thermodynamical topology, providing a clear physical interpretation. As a first step, we apply this framework to black holes in Einstein gravity, systematically elucidating their phase structure in terms of topological invariants. We then extend our analysis to black holes in 7-dimensional Lovelock gravity, where novel thermodynamic phenomena naturally emerge from the topological perspective. Moreover, we explore the connection between critical exponents and the extended thermodynamical topology, uncovering a correspondence between the zeros of the $k$-th order vector field and the associated critical exponents. Our study demonstrates that extended thermodynamical topology offers a robust and fine-grained framework for analyzing and classifying black hole phase transitions.