Photon emission from inside the innermost stable circular orbit

TL;DR

This paper investigates photon escape probabilities from a source near the ISCO of a Kerr black hole, revealing that most photons escape from a region roughly halfway between the ISCO and the event horizon, with emitter motion influencing escape and energy shifts.

Contribution

It provides a detailed analysis of photon escape regions near the ISCO, incorporating emitter motion effects and establishing conditions for photon escape in Kerr spacetime.

Findings

More than 50% of photons escape from a region halfway between ISCO and horizon.

Emitter motion increases photon escape probability and blueshifts photon energy.

Escape regions are characterized in the impact parameter space for Kerr black holes.

Abstract

We consider a situation where a light source orbiting the innermost stable circular orbit (ISCO) of the Kerr black hole is gently falling from the marginally stable orbit due to an infinitesimal perturbation. Assuming that the light source emits photons isotropically, we show that the last radius at which more than 50\% of emitted photons can escape to infinity is approximately halfway between the ISCO radius and the event horizon radius. To evaluate them, we determine emitter orbits from the vicinity of the ISCO, which are uniquely specified for each black hole spin, and identify the conditions for a photon to escape from any point on the equatorial plane of the Kerr spacetime to infinity by specifying regions in the two-dimensional photon impact parameter space completely. We further show that the proper motion of the emitter affects the photon escape probability and blueshifts the energy of emitted photons.