# Understanding photon sphere and black hole shadow in dynamically evolving spacetimes

## TL;DR

This paper derives and analyzes the evolution of photon spheres in various dynamical black hole spacetimes, highlighting their dependence on energy conditions and potential observational implications for black hole shadows.

## Contribution

It introduces a differential equation for photon sphere evolution in dynamical spacetimes and explores its solutions across different models, including rotating and higher-curvature cases.

## Key findings

- Photon sphere evolution depends on null energy condition validity.
- Black hole shadow evolution can serve as an observational test.
- Comparison between graviton and photon spheres in Einstein-Gauss-Bonnet gravity.

## Abstract

We have derived the differential equation governing the evolution of the photon sphere for dynamical black hole spacetimes with or without spherical symmetry. Numerical solution of the same depicting evolution of the photon sphere has been presented for Vaidya, Reissner-Nordstr\"{o}m-Vaidya and de-Sitter Vaidya spacetimes. It has been pointed out that evolution of the photon sphere depends crucially on the validity of the null energy condition by the in-falling matter and may present an observational window to even test it through black hole shadow. We have also presented the evolution of the photon sphere for slowly rotating Kerr-Vaidya spacetime and associated structure of black hole shadow. Finally, the effective graviton metric for Einstein-Gauss-Bonnet gravity has been presented, and the graviton sphere has been contrasted with the photon sphere in this context.