Photon emission from circular equatorial Kerr orbiters

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