论文标题
光子表面较少的对称空间
Photon surfaces in less symmetric spacetimes
论文作者
论文摘要
我们研究了光子表面及其在不太对称的时空中的稳定性，这是一种一般的静态翘曲产物，具有翘曲功能，作用于riemannian submanifold的二次拟构符。我们找到一个一维假势，将光子表面视为其极端，而不论亚策略的空间对称性如何。最大值和最小值分别对应于不稳定和稳定的光子表面。它类似于在球形时空中给出无效的圆形轨道的电势。我们还看到，对于爱因斯坦方程的解决方案的空间确实存在光子表面。指定了存在光子表面的参数值。最终显示，伪能力是由于无效的地球方程的可分离性而产生的，并且可分离性来自时空中的杀伤张量的存在。结果得出的结论是，如果时空接收杀伤量，即使在不太对称的时空中，光子表面也可能存在。
We investigate photon surfaces and their stability in a less symmetric spacetime, a general static warped product with a warping function acting on a Riemannian submanifold of codimension two. We find a one-dimensional pseudopotential that gives photon surfaces as its extrema regardless of the spatial symmetry of the submanifold. The maxima and minima correspond to unstable and stable photon surfaces, respectively. It is analogous to the potential giving null circular orbits in a spherically symmetric spacetime. We also see that photon surfaces indeed exist for the spacetimes which are solutions to the Einstein equation. The parameter values for which the photon surfaces exist are specified. As we show finally, the pseudopotential arises due to the separability of the null geodesic equation, and the separability comes from the existence of a Killing tensor in the spacetime. The result leads to the conclusion that photon surfaces may exist even in a less symmetric spacetime if the spacetime admits a Killing tensor.
