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

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.

Complete classification of photon escape in the Kerr black hole spacetime

“…We can find that the escapable region corresponds to the regions in Fig. 3 further restricted by the condition (17).…”

“…Necessary and sufficient condition for photon escape, q ≥ 0 Let us further restrict the above necessary condition for photon escape by the non-negativity of Θ, i.e., Eq. (17).…”

“…These two effects are due to the relativistic boost or beaming caused by the proper motion of the emitter, and in recent years, such relativistic effects have been actively discussed [12][13][14][15]. The analytic value of the escape probability and Doppler blueshift of various emitters were recently found by using the near-horizon geometry of the extremal Kerr black hole [11,16,17].…”