Without specifying a matter field nor imposing energy conditions, we study Killing horizons in -dimensional static solutions in general relativity with an -dimensional Einstein base manifold. Assuming linear relations and near a Killing horizon between the energy density ρ, radial pressure , and tangential pressure p2 of the matter field, we prove that any non-vacuum solution satisfying ( ) or does not admit a horizon as it becomes a curvature singularity. For and , non-vacuum solutions admit Killing horizons, on which there exists a matter field only for and , which are of the Hawking–Ellis type I and type II, respectively. Differentiability of the metric on the horizon depends on the value of , and non-analytic extensions beyond the horizon are allowed for . In particular, solutions can be attached to the Schwarzschild–Tangherlini-type vacuum solution at the Killing horizon in at least a regular manner without a lightlike thin shell. We generalize some of those results in Lovelock gravity with a maximally symmetric base manifold.

中文翻译：

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对称性静态解中 Killing 视界的存在和不存在


在不指定物质场或施加能量条件的情况下，我们用 -维爱因斯坦基流形研究广义相对论中维静态解中的 Killing 视界。假设物质场的能量密度 ρ、径向压力和切向压力 p2 之间存在线性关系并且接近杀戮视界，我们证明任何非真空解都满足 （ ） 或不承认视界，因为它成为曲率奇点。对于 和 ，非真空解接受杀戮视界，其中仅存在 和 的物质场，它们分别属于霍金-埃利斯类型 I 和 II 型。指标在水平上的可微性取决于 的值，并且允许超出水平的非分析扩展。特别是，溶液可以至少以规则的方式连接到杀戮视界的 Schwarzschild-Tangherlini 型真空溶液上，而无需轻薄壳。我们将其中一些结果推广到具有最大对称基础流形的 Lovelock 引力中。