标题： 德西特时空中的黑洞拓扑类 显示英文标题

标题： Topological classes of black holes in de-Sitter spacetime

摘要： 在本文中，我们研究了具有不同电荷$(q)$和旋转$(a)$参数的德西特黑洞解的拓扑数。 通过使用广义自由能和段的$\phi$-映射拓扑电流理论，我们发现黑洞的拓扑数仍然可以分为三种类型。 此外，我们有趣地发现，具有不同视界（即黑洞事件视界和宇宙学视界）的德西特$($dS$)$时空的拓扑类将是不同的。 此外，我们还研究了带有或不带高斯-博内特项的高维dS黑洞解的拓扑分类。 显示英文摘要

摘要： 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.