Photon surfaces extensions for dynamical gravitational collapse
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.
Cite
@article{arxiv.2509.01368,
title = {Photon surfaces extensions for dynamical gravitational collapse},
author = {Roberto Giambò and Camilla Lucamarini},
journal= {arXiv preprint arXiv:2509.01368},
year = {2026}
}
Comments
References added, Introduction and Conclusions expanded, minor corrections throughout the text