Photon surfaces extensions for dynamical gravitational collapse

2025/09/01 by Giambò, Roberto, Lucamarini, Camilla
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2509.01368

Abstract

The equations for the photon surface in spherical symmetry are worked out, starting from arXiv:gr-qc/0005050, in the most general dynamical setting. We show that the condition for a timelike hypersurface to be a photon surface can be reformulated as a non-autonomous dynamical system, whose analysis reveals that the same condition also holds when the surface is generated by a null radial geodesic. As an application, we consider a well-known model of a spherical dust cloud undergoing gravitational collapse. Comparing our findings with those in arXiv:1910.13758 we establish that the photon surface uniquely extends in the interior spacetime as a null hypersurface, allowing us to analytically investigate whether it covers the singularity developing in the LTB model.

Citations

• Analytical approach for calculating shadow of dynamical black hole
• The role of topological photon spheres in constraining the parameters of black holes
• General approach on shadow radius and photon spheres in asymptotically flat spacetimes and the impact of mass-dependent variations
• Constructing massive particles surfaces in static spacetimes
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• The geometry of photon surfaces
• Geometry of general hypersurfaces in spacetime: junction conditions

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