Topological classes of black holes in de-Sitter spacetime

TL;DR

This paper classifies the topological properties of de-Sitter black holes with various charges and rotation, revealing differences between horizons and extending to higher dimensions with Gauss-Bonnet corrections.

Contribution

It introduces a topological classification scheme for de-Sitter black holes, including multiple horizons and higher-dimensional cases with Gauss-Bonnet terms.

Findings

Black hole topological numbers can be classified into three types.

Topological classes differ between black hole and cosmological horizons.

Higher-dimensional dS black holes with Gauss-Bonnet terms exhibit distinct topological features.

Abstract

In this paper, we investigate the topological number of de-Sitter black hole solutions with different charges $(q)$ and rotational $(a)$ parameters. By using generalized free energy and Duan's $\phi$-mapping topological current theory, we find that the topological numbers of black holes can still be classified as three types. In addition, we interestingly found the topological classes for de-Sitter $($dS$)$ spacetime with distinct horizon, i.e, black hole event horizon and cosmological horizon, will be different. Moreover, we also investigate topological classifications of dS black hole solutions in higher dimensions with or without Gauss-Bonnet term.