• Accepted Paper

Photon spheres in dynamical spacetimes

David Díaz-Guerra, Ángel Rincón, and Diego Rubiera-Garcia

Phys. Rev. D - Accepted 21 October, 2026

DOI: https://doi.org/10.1103/9m2p-3wgg

Abstract

The characterization of the photon region, i.e. the region of space-time filled with unstable bound null geodesics, is critical to understand the behavior of radiation near a compact-enough object, such as black holes. However, its study has been focused on stationary space-times, neglecting dynamical scenarios such as collapsing, accreting, or evaporating black holes. In this work, we present a novel covariant approach to describe radiation in dynamical spherical space-times. Using a 2+2 decomposition, we characterize a dynamical photon sphere as the two-sphere associated with instantaneous critical turning points of non-radial null motion, where both the radial momentum and its derivative along the null ray vanish. A smooth time-dependent family of these spheres defines a photon sphere tube, which is not assumed to be a photon surface generated by null geodesics. The resulting condition is quasi-local and can be written algebraically in terms of the areal radius, the Misner-Sharp mass, and the radial pressure. We further use geodesic deviation to characterize the local radial deviation between neighboring null geodesics at each critical turning point, while distinguishing this local deviation from the global stability of an evolving null orbit. Our formulation recovers the standard photon sphere in the static limit, and we show dynamical examples like stellar collapse and accreting/evaporating scenarios.

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