Constraining photon trajectories in black hole shadows

TL;DR

This paper analyzes the photon trajectories that form the shadow of a Kerr black hole, identifying how different photon orbits and impact parameters influence the shadow boundary and potential observable imprints of the ergoregion.

Contribution

It provides a detailed mapping of shadow boundaries based on photon orbital ranges and impact parameters, highlighting differences between co-rotating and counter-rotating photons and their observational implications.

Findings

Counter-rotating photon boundary is strongly constrained compared to co-rotating.

Conditions for observing ergoregion imprints are identified.

Restrictions on black hole spin and orientation are established.

Abstract

We examine the shadow cast by a Kerr black hole, focusing on constraints on photons corresponding to different shadow boundaries. The photons are related to different orbital ranges and impact parameter values, creating a map of the shadow boundaries. Our analysis fixes also the conditions under which it is possible to observe an "imprint" of the black hole (outer) ergosurface and (outer) ergoregion on the Kerr black hole shadow boundary. The counter-rotating case resulted strongly constrained with respect to the co-rotating case, constituting a remarkable and significant difference where the counter-rotating component associated with the shadow boundary is strongly distinct from the co-rotating one. However, in this framework, even the co-rotating photons imply restrictions on conditions on the spins and planes, which are bounded by limiting values. We believe the results found here, being a tracer for the central black hole, can constitute new templates for the ongoing observations.