Photon Emission from Circular Equatorial Kerr Orbiters

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 $5/12+1/(\sqrt{5}\pi )\arctan \sqrt{5/3}\approx 54.65\%$. 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".

arXiv comment24 pages, 10 figures. v2: expanded discussion

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Cited by in corpus (13)

• Photon Ring Autocorrelations
• Polarized Image of Equatorial Emission in the Kerr Geometry
• Photon ring test of the Kerr hypothesis: Variation in the ring shape
• Adaptive Analytical Ray Tracing of Black Hole Photon Rings
• Relativistic propagation and frame dragging time delay in the timing of a pulsar orbiting the supermassive black hole SgrA*
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• Bayesian Black Hole Photogrammetry
• Photon emission from inside the innermost stable circular orbit
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• Observability of Zero-angular-momentum Sources Near Kerr Black Holes
• Photon escape in the extremal Kerr black hole spacetime
• Lumos Extrema
• Signatures of particle collisions near extreme black holes