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Register a new userPhoton emissions from NHEK and near-NHEK equatorial emitters
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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 emitters 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 emitters motion along the radial or azimuthal direction affects the PEP and the MOB of the emitted photons.
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We revisit the spectrum of linear axisymmetric gravitational perturbations of the (near-)extreme Kerr black hole. Our aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. For the near horizon region of the (near-)extreme Kerr solution, i.e. the (near-)NHEK background, we provide a complete characterisation of axisymmetric modes. This involves an infinite tower of propagating modes together with the much subtler low-lying mode sectors that contain the deformations driving the black hole away from extremality. Our analysis includes their effects on the line element, their contributions to Iyer-Wald charges around the NHEK geometry, and how to reconstitute them as gravitational perturbations on Kerr. We present in detail how regularity conditions along the angular variables modify the dynamical properties of the low-lying sector, and in particular their role in the new developments of nearly-AdS$_2$ holography.
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 emitters 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 $5/12+1/(sqrt{5}pi)arctansqrt{5/3}approx54.65%$. 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.
We have studied electromagnetic line emissions from near-horizon region in the extremal Kerr-Taub-NUT black hole spacetime and then probe the effects of NUT charge on the electromagnetic line emissions. Due to the presence of the NUT charge, the equatorial plane is no more a symmetry plane of the KTN spacetime, which leads to that the dependence of electromagnetic line emission on the NUT charge for the observer in the Southern Hemisphere differs from that in the Northern one. Our result indicate that the electromagnetic line emission in the Kerr-Taub-NUT black hole case is brighter than that in the case of Kerr black hole for the observer in the equatorial plane or in the Southern Hemisphere, but it becomes more faint as the observers position deviates far from the equatorial plane in the Northern one. Moreover, we also probe effects of redshift factor on electromagnetic emission from near-horizon region in the extremal Kerr-Taub-NUT black hole spacetime.
The region of spacetime near the event horizon of a black hole can be viewed as a deep potential well at large gravitational redshift relative to distant observers. However, matter orbiting in this region travels at relativistic speeds and can impart a significant Doppler shift to its electromagnetic emission, sometimes resulting in a net observed blueshift at infinity. Thus, a black hole broadens the line emission from monochromatic sources in its vicinity into a smoothly decaying red wing--whose flux vanishes at large redshift--together with a blue blade that retains finite flux up to a sharp edge corresponding to the maximum observable blueshift. In this paper, we study the blue blade produced by isotropic monochromatic emitters on circular equatorial orbits around a Kerr black hole, and obtain simple relations describing how the maximum blueshift encodes black hole spin and inclination. We find that small values of the maximum blueshift yield an excellent probe of inclination, while larger values provide strong constraints on spin or inclination in terms of the other. These results bear direct relevance to ongoing and future observations aiming to infer the angular momentum of supermassive black holes from the broadening of their surrounding line emission.
In this work we analyze some judiciously chosen solutions of Kerr Black Holes with Scalar Hair (KBHsSH) of special interest for Gravitational Wave (GW) events originated from Extreme Mass Ratio Inspirals (EMRIs). Because of the off-center distribution of energy density, these spacetimes are warped in such a way that not all metric functions behave monotonically on the equatorial plane as in the exterior region of Kerr black holes (KBHs). This has great impact on the orbital parameters, which in turn affects the imprints on signals descendant from EMRIs in a adiabatic evolution. By investigating circular obit parameters, we unveil what qualitative features could be present in the signals that are new and distinct compared to KBHs, and we evolve some inspirals by employing the usual quadrupole formula approximation. We show that the frequencies of the emitted signals behave nonmonotonically, i.e. they can backward chirp, and for some particular cases they can become arbitrarily small, falling below LISAs sensibility range. Finally, we present two sets of waveforms produced by a noncircular EMRI in which the compact object (CO) follows a type of geodesic motion typically present in spacetimes with a static ring (SR), in which the compact object is periodically momentarily at rest.
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