Observability of the innermost stable circular orbit in a near-extremal Kerr black hole

TL;DR

This paper investigates the escape probability of photons emitted near the ISCO of a near-extremal Kerr black hole, revealing that observable signals from near-horizon regions are possible even at high spins.

Contribution

It provides a detailed analysis of photon escape probabilities at the ISCO of rapidly rotating black holes, highlighting potential observability of near-horizon physics.

Findings

Escape probability decreases with higher black hole spin.

At the Thorne limit, escape probability is 58.8%.

At extremal spin, escape probability remains above 50%.

Abstract

We consider the escape probability of a photon emitted from the innermost stable circular orbit (ISCO) of a rapidly rotating black hole. As an isotropically emitting light source on a circular orbit reduces its orbital radius, the escape probability of a photon emitted from it decreases monotonically. The escape probability evaluated at the ISCO also decreases monotonically as the black hole spin increases. When the dimensionless Kerr parameter $a$ is at the Thorne limit $a=0.998$, the escape probability from the ISCO is $58.8\%$. In the extremal case $a=1$, even if the orbital radius of the light source is arbitrarily close to the ISCO radius, which coincides with the horizon radius, the escape probability remains at $54.6\%$. We also show that such photons that have escaped from the vicinity of the horizon reach infinity with sufficient energy to be potentially observed because Doppler blueshift due to relativistic beaming can overcome the gravitational redshift. Our findings indicate that signs of the near-horizon physics of a rapidly rotating black hole will be detectable on the edge of its shadow.