标题： 等势光子表面在任意维(电)静态时空中的研究 显示英文标题

标题： On equipotential photon surfaces in (electro-)static spacetimes of arbitrary dimension

摘要： 我们研究了$n+1$维静态、渐近平坦时空中的类时、全脐超曲面——称为光子表面——对于$n+1\geq4$。 首先，我们给出了包含（外部）次极端Reissner--Nordström时空的球对称时空类中光子表面的完整特征，因此特别地，也包括（外部）正质量Schwarzschild时空。 接下来，我们对等势光子表面附近的时空几何提供了新的见解，并给出了光子球的新特征（不依赖于任何场方程）。 此外，我们证明了任何具有由等势、（准局部）次极端光子表面和/或非退化黑洞视界组成的内边界的渐近平坦静电真空时空，必须与相同质量和电荷的必然次极端Reissner--Norström时空的适当部分等距。 我们的唯一性结果应用了Jahns的工作，并扩展和补充了几种现有的唯一性定理。 其证明主要依赖于黎曼正质量定理的较低正则性刚性情况。 显示英文摘要

摘要： We study timelike, totally umbilic hypersurfaces -- called photon surfaces -- in $n+1$-dimensional static, asymptotically flat spacetimes, for $n+1\geq4$. First, we give a complete characterization of photon surfaces in a class of spherically symmetric spacetimes containing the (exterior) subextremal Reissner--Nordstr\"om spacetimes, and hence in particular the (exterior) positive mass Schwarzschild spacetimes. Next, we give new insights into the spacetime geometry near equipotential photon surfaces and provide a new characterization of photon spheres (not appealing to any field equations). We furthermore show that any asymptotically flat electrostatic electro-vacuum spacetime with inner boundary consisting of equipotential, (quasi-locally) subextremal photon surfaces and/or non-degenerate black hole horizons must be isometric to a suitable piece of the necessarily subextremal Reissner--Norstr\"om spacetime of the same mass and charge. Our uniqueness result applies work by Jahns and extends and complements several existing uniqueness theorems. Its proof fundamentally relies on the lower regularity rigidity case of the Riemannian Positive Mass Theorem.