Photon Emission from Circular Equatorial Kerr Orbiters

TL;DR

This paper analytically investigates photon emission from circular equatorial Kerr orbiters, deriving escape probabilities and flux distributions, revealing observable signatures of near-horizon geometry in high-spin black holes.

Contribution

It introduces a new analytic framework for photon escape and flux in Kerr spacetime, including a novel near-horizon double-scaling limit for high-spin black holes.

Findings

Photon escape probability approaches approximately 54.65% for near-extremal spins.

Derived a simple formula for flux distribution on the celestial sphere.

Confirmed the near-horizon geometry of high-spin black holes is observable.

Abstract

We consider monochromatic and isotropic photon emission from circular equatorial Kerr orbiters. We derive analytic expressions for the photon escape probability and the redshift-dependent total flux collected on the celestial sphere as a function of emission radius and black hole parameters. These calculations crucially involve the critical curve delineating the region of photon escape from that of photon capture in each emitter's sky. This curve generalizes to finite orbital radius the usual Kerr critical curve and displays interesting features in the limit of high spin, which we investigate by developing a perturbative expansion about extremality. Although the innermost stable circular orbit appears to approach the event horizon for very rapidly spinning black holes, we find in this regime that the photon escape probability tends to $5/12+1/(\sqrt{5}\pi)\arctan\sqrt{5/3}\approx54.65\%$. We also obtain a simple formula for the flux distribution received on the celestial sphere, which is nonzero. This confirms that the near-horizon geometry of a high-spin black hole is in principle observable. These results require us to introduce a novel type of near-horizon double-scaling limit. We explain the dip observed in the total flux at infinity as an imprint of the black hole: the black hole "bite".