A General Discussion on Photon Spheres in Different Categories of Spacetimes

摘要: Photon sphere has attracted considerable interests in the studies of black hole and other astrophysical objects. For different categories of spacetimes (or gravitational sources), the existence of photon spheres and their distributions are dramatically influenced by geometric and topological properties of spacetimes and characteristics of the corresponding gravitational fields. In this work, we carry out a geometric analysis on photon spheres for different categories of spacetime (including black hole spacetime, ultra-compact object’s spacetime, regular spacetime, naked singularity spacetime). Some universal properties and conclusions are obtained for these spacetimes. We mostly focus on the existence of photon spheres, total number of photon spheres $n = n_{\text{stable}} + n_{\text{unstable}}$, the subtraction of stable photon sphere and unstable photon sphere $w = n_{\text{stable}} - n_{\text{unstable}}$ in different categories of spacetimes. These conclusions are derived solely from geometric properties of optical geometry of spacetimes, irrelevant to the specific spacetime metric forms. Besides, our results successfully recover some important theorems on photon spheres proposed in recent years.