Complete classification of photon escape in the Kerr black hole spacetime

TL;DR

This paper establishes the precise conditions under which photons emitted near a Kerr black hole can escape to infinity, providing a comprehensive classification of photon trajectories based on impact parameters.

Contribution

It offers a complete characterization of photon escape conditions in Kerr spacetime, including visualization tools and impact parameter space analysis.

Findings

Derived necessary and sufficient conditions for photon escape.

Identified the impact parameter space allowing photon escape.

Provided a visualization method for photon trajectory analysis.

Abstract

We consider necessary and sufficient conditions for photons emitted from the vicinity of a Kerr black hole horizon to escape to infinity. The radial equation of motion determines necessary conditions for photons to reach infinity, and the polar angle equation of motion further restricts the allowed region of photon motion. Unlike emission from the equatorial plane, the latter restrictions are crucial for photon escape when the initial polar angle of the emission point is arbitrary. We provide a visualization tool to analyze these two conditions and demonstrate a procedure for revealing photon escape. Finally, we completely identify the two-dimensional impact parameter space in which photons can escape.