Quasi-local photon surfaces in general spherically symmetric spacetimes

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