Photon emissions from near-horizon extremal and near-extremal Kerr equatorial emitters

TL;DR

This paper analyzes photon emissions from equatorial emitters near extremal Kerr black holes, providing numerical and analytical insights into photon escape probabilities and blueshifts depending on emitter motion and location.

Contribution

It offers new analytical and numerical results on photon escape probabilities and blueshifts for various emitter trajectories in near-horizon Kerr regions.

Findings

PEP exceeds 50% for anti-plunging or deflecting emitters

PEP is less than 55% for plunging emitters

PEP is always below 59% for bounded emitters in NHEK regions

Abstract

We consider isotropic and monochromatic photon emissions from equatorial emitters moving along future-directed timelike geodesics in the near-horizon extremal Kerr (NHEK) and near-horizon near-extremal Kerr (near-NHEK) regions, to asymptotic infinity. We obtain numerical results for the photon escaping probability (PEP) and derive analytical expressions for the maximum observable blueshift (MOB) of the escaping photons, both depending on the emission radius and the emitter's proper motion. In particular, we find that for all anti-plunging or deflecting emitters that can eventually reach to asymptotic infinity, the PEP is greater than $50\%$ while for all plunging emitters the PEP is less than $55\%$, and for the bounded emitters in the (near-)NHEK region, the PEP is always less than $59\%$. In addition, for the emitters on unstable circular orbits in the near-NHEK region, the PEP decreases from $55\%$ to $50\%$ as the orbital radius decreases from the one of the innermost stable circular orbit to the one of the horizon. Furthermore, we show how the orientation of the emitter's motion along the radial or azimuthal direction affects the PEP and the MOB of the emitted photons.