Dynamical photon sphere and time evolving shadow around black holes with temporal accretion

TL;DR

This paper explores the behavior of photon spheres and black hole shadows in dynamical spacetimes with accretion, specifically analyzing Vaidya black holes to understand how these structures evolve over time.

Contribution

It explicitly defines and analyzes a dynamical photon sphere in accreting black holes, extending the understanding beyond static cases.

Findings

Dynamical photon spheres exist in accreting black holes.

Photon orbits correspond to shadow edges in dynamical scenarios.

Analytical expressions for photon spheres are derived in special cases.

Abstract

A photon sphere is known as the geometrical structure shaping a black hole shadow. The mechanism is well understood for static or stationary black hole spacetimes such as the Schwarzschild and the Kerr spacetimes. In this paper, we investigate and explicitly specify a photon sphere that shapes a black hole shadow in a dynamical spacetime while taking the global structure of the spacetime into account. We consider dynamical and eternal black hole cases of the Vaidya spacetime, which represents a spherically symmetric black hole with accreting null dust. First, we numerically show that there are the dynamical photon sphere and photon orbits corresponding to the shadow edge in a moderate accretion case. Second, the photon spheres are derived analytically in special cases. Finally, we discuss the relation between our photon sphere and the several notions defined as a photon sphere generalization.