Quasi-local photon surfaces in general spherically symmetric spacetimes

Abstract

Based on the geometry of the codimension-2 surface in a general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as well as a photon surface. This new definition is the generalization of the one by Claudel, Virbhadra, and Ellis but without reference to any umbilical hypersurface in the spacetime. The new definition effectively rules out the photon surface which has noting to do with gravity. The application of the definition to the Lemaitre-Tolman-Bondi (LTB) model of gravitational collapse reduces to a problem of a second order differential equation. We find that the energy balance on the boundary of the dust ball can provide one appropriate boundary condition to this equation. Based on this key investigation, we find an analytic photon surface solution in the Oppenheimer-Snyder (OS) model and reasonable numerical solutions for the marginally bounded collapse in the LTB model. Interestingly, in the OS model, we find that the time difference between the occurrence of the photon surface and the event horizon is mainly determined by the total mass of the system but not the size or the strength of gravitational field of the system.

revtex, 19 pages, 10 figures; v3, references added, one definition is improved, typos are corrected

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Cited by in corpus (9)

• On the Size of Rotating Black Holes
• Bounds on Photon Spheres and Shadows of Charged Black Holes in Einstein-Gauss-Bonnet-Maxwell Gravity
• Gravitational lensing by a photon sphere in a Reissner-Nordström naked singularity spacetime in strong deflection limits
• Slice-reducible conformal Killing tensors, photon surfaces and shadows
• Retrolensing by light rays slightly inside and outside of a photon sphere around a Reissner-Nordström naked singularity
• Black hole shadow and Wandering null geodesics
• Quasi-local studies of the particle surfaces and their stability in general spacetimes
• Classification of static asymptotically flat spacetimes with a photon sphere in Einstein-multiple-scalar field theory
• Asymptotic behavior of null geodesics near future null infinity II: curvatures, photon surface and dynamically transversely trapping surface