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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 ϕ -mapping topological current theory, we find that the topological numbers of black holes can still be classified into three types. In addition, we interestingly found the topological classes for de-Sitter (dS) spacetime with distinct horizons, 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 the Gauss-Bonnet term.
Du et al. (Sat,) studied this question.
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