Rotating Kerr Black Hole Research Articles

A no-short scalar hair theorem for rotating Kerr black holes

If a black hole has hair, how short can this hair be? A partial answer to this intriguing question was recently provided by the ‘no-short hair’ theorem which asserts that the external fields of a spherically symmetric electrically neutral hairy black-hole configuration must extend beyond the null circular geodesic which characterizes the corresponding black-hole spacetime. One naturally wonders whether the no-short hair inequality is a generic property of all electrically neutral hairy black-hole spacetimes. In this paper we provide evidence that the answer to this interesting question may be positive. In particular, we prove that the recently discovered cloudy Kerr black-hole spacetimes—non-spherically symmetric non-static black holes which support linearized massive scalar fields in their exterior regions—also respect this no-short hair lower bound. Specifically, we analytically derive the lower bound on the effective lengths of the external bound-state massive scalar clouds (here is the peak location of the stationary bound-state scalar fields and r± are the horizon radii of the black hole). Remarkably, this lower bound is universal in the sense that it is independent of the physical parameters (proper mass and angular harmonic indices) of the exterior scalar fields. Our results suggest that the lower bound may be a general property of asymptotically flat electrically neutral hairy black-hole configurations.

Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior

We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant [Formula: see text]. We also prove the convergence of each solution to a stationary Coulomb solution. We separate a general solution into the charged, Coulomb part and the uncharged part. Convergence to the Coulomb solutions follows from the fact that the uncharged part satisfies a Morawetz estimate, i.e. that a spatially localized energy density is integrable in time. For the unchanged part, we study both the full Maxwell equation and the Fackerell–Ipser equation for one component. To treat the Fackerell–Ipser equation, we use a Fourier transform in [Formula: see text]. For the Fackerell–Ipser equation, we prove a refined Morawetz estimate that controls 3/2 derivatives with no loss near the orbiting null geodesics.

On the branching of the quasinormal resonances of near-extremal Kerr black holes

It has recently been shown by Yang et al. (Phys Rev D 87:041502(R), 2013a; Phys Rev D 88:044047, 2013b) that rotating Kerr black holes are characterized by two distinct sets of quasinormal resonances. These two families of quasinormal resonances display qualitatively different asymptotic behaviors in the extremal (\(a/M\rightarrow 1\)) black-hole limit: the zero-damping modes are characterized by relaxation times which tend to infinity in the extremal black-hole limit (\(\mathfrak {I}\omega \rightarrow 0\) as \(a/M\rightarrow 1\)), whereas the damped modes (DMs) are characterized by non-zero damping rates (\(\mathfrak {I}\omega \rightarrow \) finite-values as \(a/M\rightarrow 1\)). In this paper we refute the claim made by Yang et al. that co-rotating DMs of near-extremal black holes are restricted to the limited range \(0\le \mu \lesssim \mu _{\text {c}}\approx 0.74\), where \(\mu \equiv m/l\) is the dimensionless ratio between the azimuthal harmonic index m and the spheroidal harmonic index l of the perturbation mode. In particular, we use an analytical formula originally derived by Detweiler in order to prove the existence of DMs (damped quasinormal resonances which are characterized by finite\(\mathfrak {I}\omega \) values in the \(a/M\rightarrow 1\) limit) of near-extremal black holes in the \(\mu >\mu _{\text {c}}\) regime, the regime which was claimed by Yang et al. not to contain DMs. We show that these co-rotating DMs (in the regime \(\mu >\mu _{\text {c}}\)) are expected to characterize the resonance spectra of rapidly rotating (near-extremal) black holes with \(a/M\gtrsim 1-10^{-9}\).

Optical properties of black holes in the presence of a plasma: The shadow

We have studied photon motion around axially symmetric rotating Kerr black hole in the presence of plasma with radial power-law density. It is shown that in the presence of plasma the observed shape and size of shadow changes depending on i) plasma parameters, ii) black hole spin and iii) inclination angle between observer plane and axis of rotation of black hole. In order to extract pure effect of plasma influence on black hole image the particular case of the Schwarzschild black hole has also been investigated and it has been shown that i) the photon sphere around the spherical symmetric black hole is left unchanged under the plasma influence, ii) however the Schwarzschild black hole shadow size in plasma is reduced due to the refraction of the electromagnetic radiation in plasma environment of black hole. The study of the energy emission from the black hole in plasma shows that in the presence of plasma the maximal energy emission rate from the black hole decreases.

The large-mass limit of cloudy black holes

The interplay between black holes and fundamental fields has attracted much attention over the years from both physicists and mathematicians. In this paper we study analytically a physical system that is composed of massive scalar fields linearly coupled to a rapidly rotating Kerr black hole. Using simple arguments, we first show that the coupled black hole-scalar field system may possess stationary bound-state resonances (stationary scalar ‘clouds’) in the bounded regime , where μ and m are respectively the mass and azimuthal harmonic index of the field, and is the angular velocity of the black-hole horizon. We then show explicitly that these two bounds on the dimensionless ratio can be saturated in the asymptotic limit. In particular, we derive a remarkably simple analytical formula for the resonance mass spectrum of the stationary bound-state scalar clouds in the regime of large field masses: , where τ is the dimensionless temperature of the rapidly rotating (near extremal) black hole, is a constant, and is the resonance parameter. In addition, it is shown that, contrary to the flat-space intuition, the effective lengths of the scalar field configurations in the curved black-hole spacetime approach a finite asymptotic value in the large mass limit. In particular, we prove that in the large mass limit, the characteristic length scale of the scalar clouds scales linearly with the black-hole temperature.

Overspinning a Kerr black hole: The effect of the self-force

We study the scenario in which a massive particle is thrown into a rapidly rotating Kerr black hole in an attempt to spin it up beyond its extremal limit, challenging weak cosmic censorship. We work in black-hole perturbation theory, and focus on nonspinning, uncharged particles sent in on equatorial orbits. We first identify the complete parameter-space region in which overspinning occurs when backreaction effects from the particle's self-gravity are ignored. We find, in particular, that overspinning can be achieved only with particles sent in from infinity. Gravitational self-force effects may prevent overspinning by radiating away a sufficient amount of the particle's angular momentum (``dissipative effect''), and/or by increasing the effective centrifugal repulsion, so that particles with suitable parameters never get captured (``conservative effect''). We analyze the full effect of the self-force, thereby completing previous studies by Jacobson and Sotiriou (who neglected the self-force) and by Barausse, Cardoso and Khanna (who considered the dissipative effect on a subset of orbits). Our main result is an inequality, involving certain self-force quantities, which describes a necessary and sufficient condition for the overspinning scenario to be overruled. This ``censorship'' condition is formulated on a certain one-parameter family of geodesics in the limit of an extremal Kerr geometry. We find that the censorship condition is insensitive to the dissipative effect (within the first-order self-force approximation used here), except for a subset of perfectly fine-tuned orbits, for which a separate censorship condition is derived. We do not obtain here the self-force input needed to evaluate either of our two conditions, but discuss the prospects for producing the necessary data using state-of-the-art numerical codes.

Dynamics of a charged particle around a slowly rotating Kerr black hole immersed in magnetic field

The dynamics of a charged particle moving around a slowly rotating Kerr black hole in the presence of an external magnetic field is investigated. We are interested to explore the conditions under which the charged particle can escape from the gravitational field of the black hole after colliding with another particle. The escape velocity of the charged particle in the innermost stable circular orbit is calculated. The effective potential and escape velocity of the charged particle with angular momentum in the presence of magnetic field is analyzed. This work serves as an extension of a preceding paper dealing with the Schwarzschild black hole [Zahrani {\it et al}, Phys. Rev. D 87, 084043 (2013)].

NO EVIDENCE FOR BARDEEN-PETTERSON ALIGNMENT IN GRMHD SIMULATIONS AND SEMI-ANALYTIC MODELS OF MODERATELY THIN, PROGRADE, TILTED ACCRETION DISKS

In this paper we introduce the first results that use data extracted directly from numerical simulations as inputs to the analytic twisted disk model of Zhuravlev & Ivanov. In both numerical and analytic approaches, fully relativistic models of tilted and twisted disks having a moderate effective viscosity around a slowly rotating Kerr black hole are considered. Qualitatively, the analytic model demonstrates the same dynamics as the simulations, although with some quantitative offset. Namely, the GRMHD simulations generally give smaller variations of tilt and twist across the disk. When the black hole and the disk rotate in the same sense, the simulated tilted disk and analytic model show no sign of Bardeen-Petterson alignment, even in the innermost parts of the disk, where the characteristic time for relaxation to a quasi-stationary configuration is of the same order as the computation time. In the opposite case, when the direction of the disk's rotation is opposite to that of black hole, a partial alignment is observed, in agreement with previous theoretical estimates. Thus, both fully numerical and analytic schemes demonstrate that the Bardeen-Petterson effect may not be possible for the case of prograde rotation provided that disk's effective viscosity is sufficiently small. This may have implications in modeling of different astrophysical phenomena, such as disk spectra and jet orientation.

Greybody factors for Myers–Perry black holes

The Myers–Perry black holes are higher-dimensional generalizations of the usual (3+1)-dimensional rotating Kerr black hole. They are of considerable interest in Kaluza–Klein models, specifically within the context of brane-world versions thereof. In the present article, we shall consider the greybody factors associated with scalar field excitations of the Myers–Perry spacetimes, and develop some rigorous bounds on these greybody factors. These bounds are of relevance for characterizing both the higher-dimensional Hawking radiation, and the super-radiance, that is expected for these spacetimes.

New studies of tunneling radiation from Kerr-Newman black holes

In the paper [Wu D et al. Sci. sin. G: Phys. Mech. Astron. 43 115], starting from the action of a massive particle's Lagrangian, we have made a new, unified derivation of the timelike and null geodesics of a rotating Kerr black hole. Our results demonstrate that one need not constrain himself to adopt the dragging coordinate system to investigate the tunneling radiation of rotating black holes. That work completely overcomes all shortcomings existing in the previous related researches, thus making Parikh-Wilczek's semi-classical approach more perfect and consistent. In this paper, we extend that work to the case of a rotating charged black hole to present a new derivation of the geodesic equation of a massive charged particle in the Kerr-Newman black hole and to reinvestigate its tunneling radiation.

Marginally bound (critical) geodesics of rapidly rotating black holes

One of the most important geodesics in a black hole spacetime is the marginally bound spherical orbit. This critical geodesic represents the innermost spherical orbit which is bound to the central black hole. The radii ${r}_{\mathrm{mb}}(\overline{a})$ of the marginally bound equatorial circular geodesics of rotating Kerr black holes were found analytically by Bardeen et al. more than four decades ago (here $\overline{a}\ensuremath{\equiv}J/{M}^{2}$ is the dimensionless angular momentum of the black hole). On the other hand, no closed-form formula exists in the literature for the radii of generic (nonequatorial) marginally bound geodesics of the rotating Kerr spacetime. In the present study, we analyze the critical (marginally bound) orbits of rapidly rotating Kerr black holes. In particular, we derive a simple analytical formula for the radii ${r}_{\mathrm{mb}}(\overline{a}\ensuremath{\simeq}1;\mathrm{cos}i)$ of the marginally bound spherical orbits, where $\mathrm{cos}i$ is an effective inclination angle (with respect to the black hole equatorial plane) of the geodesic. We find that the marginally bound spherical orbits of rapidly rotating black holes are characterized by a critical inclination angle, $\mathrm{cos}i=\sqrt{2/3}$, above which the coordinate radii of the geodesics approach the black hole radius in the extremal $\overline{a}\ensuremath{\rightarrow}1$ limit. It is shown that this critical inclination angle signals a transition in the physical properties of the orbits: in particular, it separates marginally bound spherical geodesics which lie a finite proper distance from the black hole horizon from marginally bound geodesics which lie an infinite proper distance from the horizon.

Escape of superheavy and highly energetic particles produced by particle collisions near maximally charged black holes

For particle collision near rapidly rotating Kerr black holes, the center-of-mass energy can be arbitrarily high if the angular momentum of either of the colliding particles is fine-tuned. Recently, it has been shown that particles which are produced by such a particle collision and escape to infinity cannot be very massive nor very energetic. For electrically charged black holes there is a similar phenomenon, where the center-of-mass energy for the collision of charged particles near the horizon can be arbitrarily high. One might expect that there would exist a similar bound on the energy and mass of particles that are produced by such a particle collision and escape to infinity. In this paper, however, we see that this expectation is not the case. We explicitly show that superheavy and highly energetic charged particles produced by the collision near maximally charged black holes can escape to infinity at least within classical theory if the backreaction and self-force of the particle can be neglected.

Black-hole perturbation theory: The asymptotic spectrum of the prolate spin-weighted spheroidal harmonics

Prolate spin-weighted spheroidal harmonics play a key role in black-hole perturbation theory. In particular, the highly damped quasinormal resonances of rotating Kerr black holes are closely related to the asymptotic eigenvalues of these important functions. We here present a novel and compact derivation of the asymptotic eigenvalues of the prolate spin-weighted spheroidal harmonics. Our analysis is based on a simple trick which transforms the corresponding spin-weighted spheroidal angular equation into a Schr\"odinger-like wave equation which is amenable to a standard WKB analysis. Our analytical results for the prolate asymptotic spectrum agree with previous numerical computations of the eigenvalues which appear in the literature.

Spherical null geodesics of rotating Kerr black holes

The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature for the radii of generic (non-equatorial) spherical geodesics. We provide here an approximate formula for the radii rph(a/M;cosi) of these spherical null geodesics, where a/M is the dimensionless angular momentum of the black hole and cosi is an effective inclination angle (with respect to the black-hole equatorial plane) of the orbit. It is well-known that the equatorial circular geodesics of the Kerr spacetime (the prograde and the retrograde orbits with cosi=±1) are characterized by a monotonic dependence of their radii rph(a/M;cosi=±1) on the dimensionless spin-parameter a/M of the black hole. We use here our novel analytical formula to reveal that this well-known property of the equatorial circular geodesics is actually not a generic property of the Kerr spacetime. In particular, we find that counter-rotating spherical null orbits in the range (33−59)/4≲cosi<0 are characterized by a non-monotonic dependence of rph(a/M;cosi=const) on the dimensionless rotation-parameter a/M of the black hole. Furthermore, it is shown that spherical photon orbits of rapidly-rotating black holes are characterized by a critical inclination angle, cosi=4/7, above which the coordinate radii of the orbits approach the black-hole radius in the extremal limit. We prove that this critical inclination angle signals a transition in the physical properties of the spherical null geodesics: in particular, it separates orbits which are characterized by finite proper distances to the black-hole horizon from orbits which are characterized by infinite proper distances to the horizon.

No-bomb theorem for charged Reissner–Nordström black holes

The fundamental role played by black holes in many areas of physics makes it highly important to explore the nature of their stability. The stability of charged Reissner–Nordström black holes to neutral (gravitational and electromagnetic) perturbations was established almost four decades ago. However, the stability of these charged black holes under charged perturbations has remained an open question due to the complexity introduced by the well-known phenomena of superradiant scattering: A charged scalar field impinging on a charged Reissner–Nordström black hole can be amplified as it scatters off the hole. If the incident field has a non-zero rest mass, then the mass term effectively works as a mirror, preventing the energy extracted from the hole from escaping to infinity. One may suspect that the superradiant amplification of charged fields by the charged black hole may lead to an instability of the Reissner–Nordström spacetime (in as much the same way that rotating Kerr black holes are unstable under rotating scalar perturbations). However, in this Letter we show that, for charged Reissner–Nordström black holes in the regime (Q/M)2⩽8/9, the two conditions which are required in order to trigger a possible superradiant instability [namely: (1) the existence of a trapping potential well outside the black hole, and (2) superradiant amplification of the trapped modes] cannot be satisfied simultaneously. Our results thus support the stability of charged Reissner–Nordström black holes under charged scalar perturbations in the regime (Q/M)2⩽8/9.

Stationary scalar clouds around rotating black holes

Motivated by novel results in the theory of wave dynamics in black-hole spacetimes, we analyze the dynamics of a massive scalar field surrounding a rapidly rotating Kerr black hole. In particular, we report on the existence of stationary (infinitely long-lived) regular field configurations in the background of maximally rotating black holes. The effective height of these scalar ``clouds'' above the central black hole is determined analytically. Our results support the possible existence of stationary scalar field dark matter distributions surrounding rapidly rotating black holes.

A vector field method approach to improved decay for solutions to the wave equation on a slowly rotating Kerr black hole

We prove that sufficiently regular solutions to the wave equationgK� = 0 on the exterior of a sufficiently slowly rotating Kerr black hole obey the estimates |�| � C(t � ) 3 2 +� on a compact region of r. This is proved with the help of a new vector field commutator that is analogous to the scaling vector field on Minkowski and Schwarzschild spacetime. This result improves the known robust decay rates that are proved using the vector field method in the region of finite r and along the event horizon.

Black-Hole Bombs and Photon-Mass Bounds

Generic extensions of the standard model predict the existence of ultralight bosonic degrees of freedom. Several ongoing experiments are aimed at detecting these particles or constraining their mass range. Here we show that massive vector fields around rotating black holes can give rise to a strong superradiant instability, which extracts angular momentum from the hole. The observation of supermassive spinning black holes imposes limits on this mechanism. We show that current supermassive black-hole spin estimates provide the tightest upper limits on the mass of the photon (m(v) is < or approximately equal to 4×10(-20) eV according to our most conservative estimate), and that spin measurements for the largest known supermassive black holes could further lower this bound to m(v) < or approximately equal to 10(-22) eV. Our analysis relies on a novel framework to study perturbations of rotating Kerr black holes in the slow-rotation regime, that we developed up to second order in rotation, and that can be extended to other spacetime metrics and other theories.

Erratum: Upper limits of particle emission from high-energy collision and reaction near a maximally rotating Kerr black hole [Phys. Rev. D86, 024027 (2012)PRVDAQ1550-7998

Erratum: Upper limits of particle emission from high-energy collision and reaction near a maximally rotating Kerr black hole [Phys. Rev. D<b>86</b>, 024027 (2012)PRVDAQ1550-7998

Resonance spectrum of near-extremal Kerr black holes in the eikonal limit

The fundamental resonances of rapidly rotating Kerr black holes in the eikonal limit are derived analytically. We show that there exists a critical value, μc=15−1932, for the dimensionless ratio μ≡m/l between the azimuthal harmonic index m and the spheroidal harmonic index l of the perturbation mode, above which the perturbations become long lived. In particular, it is proved that above μc the imaginary parts of the quasinormal frequencies scale like the black-hole temperature: ωI(n;μ>μc)=2πTBH(n+12). This implies that for perturbations modes in the interval μc<μ⩽1, the relaxation period τ∼1/ωI of the black hole becomes extremely long as the extremal limit TBH→0 is approached. A generalization of the results to the case of scalar quasinormal resonances of near-extremal Kerr–Newman black holes is also provided. In particular, we prove that only black holes that rotate fast enough (with MΩ⩾25, where M and Ω are the black-hole mass and angular velocity, respectively) possess this family of remarkably long-lived perturbation modes.