Spherically, plane, or hyperbolically symmetric spacetimes with an additional hypersurface orthogonal Killing vector are often called “static” spacetimes even if they contain regions where the Killing vector is nontimelike. It seems to be widely believed that an energy-momentum tenor for a matter field compatible with these spacetimes in general relativity is of the Hawking-Ellis type I everywhere. We show in arbitrary $n(\ge 3)$ dimensions that, contrary to popular belief, a matter field on a Killing horizon is not necessarily of type I but can be of type II. Such a type-II matter field on a Killing horizon is realized in the Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole in the Einstein-Maxwell-dilaton system and may be interpreted as a mixture of a particular anisotropic fluid and a null dust fluid.

中文翻译：

---

对称时空中杀死视界上的霍金-埃利斯类型的物质

球面、平面或双曲对称时空以及额外的超曲面正交杀伤向量通常被称为“静态”时空，即使它们包含杀伤向量非时空的区域。人们似乎普遍认为，与广义相对论中的这些时空兼容的物质场的能量-动量基调在任何地方都属于霍金-埃利斯 I 型。我们在任意显示$n(\ge 3)$与流行的看法相反，Killing 视界上的物质场不一定是 I 型，但可以是 II 型。Killing 视界上的这种 II 型物质场在爱因斯坦-麦克斯韦-扩张系统的 Gibbons-Maeda-Garfinkle-Horowitz-Strominger 黑洞中实现，可以解释为特定各向异性流体和零尘的混合物体液。