Universal thermodynamic topological classes of rotating black holes

TL;DR

This paper applies a universal topological classification scheme to various rotating black holes, revealing their thermodynamic stability properties and confirming the classification conjecture across different dimensions and charges.

Contribution

It extends the topological classification of black hole thermodynamics to higher dimensions and charged black holes, confirming the universality of the scheme.

Findings

Higher-dimensional Kerr black holes are thermodynamically unstable at small sizes.

Four-dimensional Kerr-Newman black holes have stable small black hole states.

Different black hole classes are identified based on their thermodynamic stability patterns.

Abstract

In a recent study, Wei et al. [Phys. Rev. D 110, L081501 (2024)] proposed a universal classification scheme that interprets black hole solutions as topological defects within the thermodynamic parameter space, and then divides black hole solutions into four distinct classes, denoted as $W^{1-}$, $W^{0+}$, $W^{0-}$, and $W^{1+}$, offering insights into deeper aspects of black hole thermodynamics and gravity. In this paper, we investigate the universal thermodynamic topological classification of the singly rotating Kerr black holes in all dimensions, as well as the four-dimensional Kerr-Newman black hole. We show that the innermost small black hole states of the $d \geq 6$ singly rotating Kerr black holes are thermodynamically unstable, while those of the four-dimensional Kerr-Newman black hole and the $d = 4, 5$ singly rotating Kerr black holes are thermodynamically stable. On the other hand, the outermost large black holes exhibit unstable behavior in all these cases. At the low-temperature limit, the $d \geq 6$ singly rotating Kerr black holes have one large thermodynamically unstable black hole, while the four-dimensional Kerr-Newman black hole and the $d = 4, 5$ singly rotating Kerr black holes feature one large unstable branch and one small stable branch. Conversely, at the high-temperature limit, the $d \geq 6$ singly rotating Kerr black holes exhibit a small unstable black hole state, while the four-dimensional Kerr-Newman black hole and the $d = 4, 5$ singly rotating Kerr black holes have no black hole states at all. Consequently, we demonstrate that the $d \geq 6$ singly rotating Kerr black holes belong to the class $W^{1-}$, whereas the four-dimensional Kerr-Newman and $d = 4, 5$ singly rotating Kerr black holes belong to the class $W^{0+}$, thereby further support the conjecture proposed in [Phys. Rev. D 110, L081501 (2024)].