Topological classes of rotating black holes

TL;DR

This paper explores the topological classification of rotating black holes across different dimensions, revealing how rotation and spacetime dimension influence their topological numbers, and supports a conjecture on black hole topological classes.

Contribution

It provides a detailed analysis of topological numbers for various rotating black holes, confirming the conjecture that black holes fall into three topological classes within Einstein-Maxwell gravity.

Findings

Rotation significantly affects topological numbers.

Spacetime dimension influences topological classification.

Electric charge has no effect on topological number.

Abstract

In this paper, we investigate the topological numbers for singly rotating Kerr black holes in arbitrary dimensions and four-dimensional Kerr-Newman black hole. We show that for uncharged black holes, the rotation parameter has a significant effect on the topological number, and for rotating black holes, the dimension of spacetime has a remarkable effect on the topological number too. In addition, we find that the topological numbers of the four-dimensional Kerr and Kerr-Newman black holes are the same, which seems to indicate that the electric charge parameter has no effect on the topological number of rotating black holes. Our current research provides more evidence that the conjecture put forward in Wei et al. [Phys. Rev. Lett. 129, 191101 (2022)], according to which all black hole solutions should be separated into three different topological classes, is accurate, at least in the pure Einstein-Maxwell gravity theory.