Universal thermodynamic topological classes of black holes in perfect fluid dark matter background

TL;DR

This paper classifies black holes in a perfect fluid dark matter background into four universal thermodynamic classes, revealing their stability and phase behavior across different black hole types and temperature regimes.

Contribution

It extends the universal thermodynamic classification framework to black holes in PFDM, identifying their specific topological classes and stability characteristics.

Findings

Schwarzschild black hole in PFDM belongs to class W^{1-}

Reissner-Nordstr"om, Kerr, Kerr-Newman black holes in PFDM are in class W^{0+}

Kerr-AdS black hole belongs to class W^{1+}

Abstract

In this paper, we study the universal thermodynamic topological classes of a family of black holes in a perfect fluid dark matter (PFDM) background. Recent research on black hole thermodynamics suggests that all black holes can be classified into four universal thermodynamic classes, denoted by $W^{1-}$, $W^{0+}$, $W^{0-}$, and $W^{1+}$. Our study reveals that the Schwarzschild black hole in PFDM belongs to the $W^{1-}$ class, and independence of black hole size thermodynamically unstable at both low- and high-temperature limits. The Reissner-Nordstr\"om, Kerr, and Kerr-Newman black holes in the PFDM background belong to the same universal thermodynamic class, $W^{0+}$, which represents small, stable black holes and large, unstable black holes at low-temperature limits, whereas no black hole state exists at high temperatures. The AdS black holes behave differently compared to their counterparts in PFDM. The Schwarzschild-AdS black hole belongs to the $W^{0-}$ class, indicating no black hole state at low temperatures, but small, unstable and large, stable black hole states at high temperatures. Furthermore, the Kerr-AdS black hole belongs to the $W^{1+}$ class, characterized by small, stable black holes at low temperatures, large, stable black holes at high temperatures, and unstable, intermediate-sized black holes at both low and high temperatures. These findings uncover the universal topological classifications underlying black hole thermodynamics, offering profound insights into the fundamental principles of quantum gravity.