Near-extremal Kerr Black Holes Research Articles

Destroying a near-extremal Kerr black hole with a charged particle: Can a test magnetic field serve as a cosmic censor?

We investigate effect of a test magnetic field on the process of destroying near-extremal Kerr black hole with a charged test particle. It has been shown that it would be possible to throw a charged test particle into the near extremal rotating black hole and make it go past the extremality i.e. turn Kerr black hole into the Kerr-Newmann naked singularity. Typically in an astrophysical scenario black holes are believed to be surrounded by a magnetic field. Magnetic field although small, affects motion of charged particles drastically due to the large Lorentz force, as the electromagnetic force is much stronger that the gravity. Thus a test magnetic field can affect the process of destroying black holes and restore the cosmic censorship in the astrophysical context. We show that a test magnetic field would act as a cosmic censor beyond a certain threshold value. We try to gauge the magnitude of the magnetic field by comparing its energy density with that of the change in the curvature induced by the test particle. We find that the magnetic field required in only as strong as or slightly stronger as compared to the value for which its effect of the background geometry is comparable to the tiny backreaction as that of the test particle. In such a case however one has to take take into account effect of the magnetic field on the background geometry, which is difficult to implement in the absence of any exact near-extremal rotating magnetized black hole solutions. We argue that magnetic field would still act as a cosmic censor.

Gravity waves from extreme-mass-ratio plunges into Kerr black holes

Massive objects orbiting a near-extreme Kerr black hole quickly plunge into the horizon after passing the innermost stable circular orbit. The plunge trajectory is shown to be related by a conformal map to a circular orbit. Conformal symmetry of the near-horizon region is then used to compute the gravitational radiation produced during the plunge phase.

Unbound geodesics from the ergosphere and potential observability of debris from ultrahigh energy particle collisions

Particle collisions in black hole ergoregions may result in extremely high center-of-mass energies that could probe new physics if escape to infinity were possible. Here we show that some geodesics at high inclinations to the equatorial plane may be unbound. Hence a finite flux of annihilation debris is able to escape, especially in the case of near-extremal Kerr black holes and if the Penrose process plays a role. For a class of Penrose processes, we show that the Wald inequalities are satisfied, allowing the Penrose process to have a key role in high-energy ejection. Hence the possibility of observing new physics effects from a black hole accelerator at unprecedentedly high particle collision energies remains a tantalizing, if futuristic, experimental vision.

CONFIRMATION VIA THE CONTINUUM-FITTING METHOD THAT THE SPIN OF THE BLACK HOLE IN CYGNUS X-1 IS EXTREME

In Gou et al. (2011), we reported that the black hole primary in the X-ray binary Cygnus X-1 is a near-extreme Kerr black hole with a spin parameter a*>0.95(3{\sigma}). We confirm this result while setting a new and more stringent limit: a*>0.983 at the 3{\sigma}(99.7%) level of confidence. The earlier work, which was based on an analysis of all three useful spectra that were then available, was possibly biased by the presence in these spectra of a relatively strong Compton power-law component: The fraction of the thermal seed photons scattered into the power law was f_s=23-31%, while the upper limit for reliable application of the continuum-fitting method is f_s<25%. We have subsequently obtained six additional spectra of Cygnus X-1 suitable for the measurement of spin. Five of these spectra are of high quality with f_s in the range 10% to 19%, a regime where the continuum-fitting method has been shown to deliver reliable results. Individually, the six spectra give lower limits on the spin parameter that range from a*>0.95 to a*>0.98, allowing us to conservatively conclude that the spin of the black hole is a*>0.983 (3{\sigma}).

ABSORPTION OF A PARTICLE BY A ROTATING BLACK HOLE

We examine the absorption of a test particle by a near-extreme Kerr black hole, including both positive and negative energy particles. Allowing arbitrary values of the particle's radial momentum at the horizon, we display the region in which the absorption of the particle would "overspin" the black hole and also the region in which it would reduce the area of the black hole. The portions of these regions for a positive energy particle, shrink and disappear as the angular momentum of the initial black hole approaches the extreme Kerr limit. But even in that limit the absorption of a negative energy particle can reduce the area. Proposals to go beyond the test particle approximation are also discussed.

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.

THE EXTREME SPIN OF THE BLACK HOLE IN CYGNUS X-1

The compact primary in the X-ray binary Cygnus X-1 was the first black hole to be established via dynamical observations. We have recently determined accurate values for its mass and distance, and for the orbital inclination angle of the binary. Building on these results, which are based on our favored (asynchronous) dynamical model, we have measured the radius of the inner edge of the black hole's accretion disk by fitting its thermal continuum spectrum to a fully relativistic model of a thin accretion disk. Assuming that the spin axis of the black hole is aligned with the orbital angular momentum vector, we have determined that Cygnus X-1 contains a near-extreme Kerr black hole with a spin parameter a/M>0.95 (3\sigma). For a less probable (synchronous) dynamical model, we find a/M>0.92 (3\sigma). In our analysis, we include the uncertainties in black hole mass, orbital inclination angle and distance, and we also include the uncertainty in the calibration of the absolute flux via the Crab. These four sources of uncertainty totally dominate the error budget. The uncertainties introduced by the thin-disk model we employ are particularly small in this case given the extreme spin of the black hole and the disk's low luminosity.

Quasinormal resonances of a massive scalar field in a near-extremal Kerr black hole spacetime

The fundamental resonances of near-extremal Kerr black holes due to massive scalar perturbations are derived analytically. We show that there exists a critical mass parameter, ${\ensuremath{\mu}}_{c}$, below which increasing the mass $\ensuremath{\mu}$ of the field increases the oscillation frequency $\ensuremath{\mathfrak{R}}(\ensuremath{\omega})$ of the resonance. On the other hand, above the critical field mass increasing the mass $\ensuremath{\mu}$ increases the damping rate $\ensuremath{\mathfrak{I}}(\ensuremath{\omega})$ of the mode. We confirm our analytical results by numerical computations.

Conformal weights in the Kerr/CFT correspondence

It has been conjectured that a near-extreme Kerr black hole is described by a 2d CFT. Previous work has shown that CFT operators dual to axisymmetric gravitational perturbations have integer conformal weights. In this paper, we study the analogous problem in 5d. We consider the most general near-extreme vacuum black hole with two rotational symmetries. This includes Myers-Perry black holes, black rings and Kaluza-Klein black holes. We find that operators dual to gravitational (or electromagnetic or massless scalar field) perturbations preserving both rotational symmetries have integer conformal weights, the same for all black holes considered.

A NEAR-NHEK/CFT CORRESPONDENCE

We consider excitations around the recently introduced near-NHEK metric describing the near-horizon geometry of the near-extremal four-dimensional Kerr black hole. This geometry has a U (1)L × U (1)R isometry group which can be enhanced to a pair of commuting Virasoro algebras. We present boundary conditions for which the conserved charges of the corresponding asymptotic symmetries are well defined and nonvanishing and find the central charges cL = 12J/ℏ and cR = 0 where J is the angular momentum of the black hole. Applying the Cardy formula reproduces the Bekenstein–Hawking entropy of the black hole. This suggests that the near-extremal Kerr black hole is holographically dual to a nonchiral two-dimensional conformal field theory.

Real-time correlators in Kerr/CFT correspondence

We study real-time correlators in the Kerr/CFT correspondence. The near-horizon geometry of extreme and near-extremal Kerr black holes can be taken as warped spacetimes with the warping factors depending on the transverse radius and the angular variable. By considering the Kerr/CFT correspondence as a generalized warped AdS/CFT correspondence, we show how to compute the CFT real-time correlation functions. We find that the retarded Green's functions, the cross sections and the quasi-normal modes are all in perfect match with the predictions of the dual CFT. The same analysis is also generalized to the charged Newman-Kerr black holes .

Black hole superradiance from Kerr/CFT

The superradiant scattering of a scalar field with frequency and angular momentum (\omega,m) by a near-extreme Kerr black hole with mass and spin (M,J) was derived in the seventies by Starobinsky, Churilov, Press and Teukolsky. In this paper we show that for frequencies scaled to the superradiant bound the full functional dependence on (\omega,m,M,J) of the scattering amplitudes is precisely reproduced by a dual two-dimensional conformal field theory in which the black hole corresponds to a specific thermal state and the scalar field to a specific operator. This striking agreement corroborates a conjectured Kerr/CFT correspondence.

Holographic derivation of Kerr-Newman scattering amplitudes for general charge and spin

Near-superradiant scattering of charged scalars and fermions by a near-extreme Kerr-Newman black hole and photons and gravitons by a near-extreme Kerr black hole are computed as certain Fourier transforms of correlators in a two-dimensional conformal field theory. The results agree with the classic spacetime calculations from the 1970s, thereby providing good evidence for a conjectured Kerr-Newman/CFT correspondence.

Black-hole quasinormal resonances: Wave analysis versus a geometric-optics approximation

It has long been known that null unstable geodesics are related to the characteristic modes of black holes-- the so called quasinormal resonances. The basic idea is to interpret the free oscillations of a black hole in the eikonal limit in terms of null particles trapped at the unstable circular orbit and slowly leaking out. The real part of the complex quasinormal resonances is related to the angular velocity at the unstable null geodesic. The imaginary part of the resonances is related to the instability timescale (or the inverse Lyapunov exponent) of the orbit. While this geometric-optics description of the black-hole quasinormal resonances in terms of perturbed null {\it rays} is very appealing and intuitive, it is still highly important to verify the validity of this approach by directly analyzing the Teukolsky wave equation which governs the dynamics of perturbation {\it waves} in the black-hole spacetime. This is the main goal of the present paper. We first use the geometric-optics technique of perturbing a bundle of unstable null rays to calculate the resonances of near-extremal Kerr black holes in the eikonal approximation. We then directly solve the Teukolsky wave equation (supplemented by the appropriate physical boundary conditions) and show that the resultant quasinormal spectrum obtained directly from the wave analysis is in accord with the spectrum obtained from the geometric-optics approximation of perturbed null rays.

Challenging the generalized second law

The generalized second law (GSL) of black hole thermodynamics states that the sum of changes in black hole entropy and the ordinary entropy of matter and fields outside the hole must be non-negative. In the classical limit, the GSL reduces to Hawking's area theorem. Neither law identifies the specific effects that make it work in particular situations. Motivated by Davies' recent gedanken experiment he used to infer a bound on the size of the fine structure constant from the GSL, we study a series of variants in which an electric test charge is lowered to a finite radius and then dropped into a Schwarzschild, a near-extremal magnetic Reissner-Nordstr\"om or a near-extremal Kerr black hole. For a classical charge, we demonstrate that a specific ``backreaction'' effect is responsible for protecting the area theorem in the near-extremal examples. For the magnetically charged Reissner-Nordstr\"om hole an area theorem violation is defused by taking into account a subtle source of repulsion of the charge: the spinning up of the black hole in the process of bringing the charge down to its dropping point. In Kerr hole case, the electric self-force on the charge is sufficient to right matters. However, in all experiments involving an elementary charge, the full GSL would apparently be violated were the fine structure constant greater than about order unity. We argue that in this case a quantum effect, the Unruh-Wald quantum buoyancy, may protect the GSL.

Slow relaxation of rapidly rotating black holes

We study analytically the relaxation phase of perturbed, rapidly rotating black holes. In particular, we derive a simple formula for the fundamental quasinormal resonances of near-extremal Kerr black holes. The formula is expressed in terms of the black hole physical parameters: $\ensuremath{\omega}=m\ensuremath{\Omega}\ensuremath{-}i2\ensuremath{\pi}{T}_{\mathrm{BH}}(n+\frac{1}{2})$, where ${T}_{\mathrm{BH}}$ and $\ensuremath{\Omega}$ are the temperature and angular velocity of the black hole, and $m$ is the azimuthal harmonic index of a corotating equatorial mode. This formula implies that the relaxation period $\ensuremath{\tau}\ensuremath{\sim}1/\ensuremath{\mathfrak{I}}\ensuremath{\omega}$ of the black hole becomes extremely long as the extremal limit ${T}_{\mathrm{BH}}\ensuremath{\rightarrow}0$ is approached. The analytically derived formula is shown to agree with direct numerical computations of the black hole resonances. We use our results to demonstrate analytically the fact that near-extremal Kerr black holes saturate the recently proposed universal relaxation bound.

Mass estimate of the XTE J1650-500 black hole from the extended orbital resonance model for high-frequency QPOs

Context. XTE J1650-500 is a Galactic black-hole binary system for which at least one high-frequency QPO at 250 Hz was reported. Moreover there are indications that the system harbours a near-extreme Kerr black-hole with a spin a∗ ≃ 0.998 and mass MBH . 7.3 M⊙. Recently it was discovered that the orbital 3-velocity of t est-particle (geodesical) discs orbiting Kerr black holes with the spin a∗ > 0.9953, being analyzed in the locally non-rotating frames, reveals a hump near the marginally stable orbit. Further it was suggested that the hump could excite the epicyclic motion of particles near the ISCO with frequencies typical for high-frequency QPOs. Characteristic frequency of the hump-induced oscillations was defined as the maximal positive rate of change of th e LNRFrelated orbital velocity with the proper radial distance. I f the characteristic “humpy frequency” and the radial epicyclic frequency are commensurable, strong resonant phenomena are expected. Aims. Application of the idea of hump-induced oscillations in accretion discs around near-extreme Kerr black holes to estimate the black-hole mass in XTE J1650-500 binary system. Methods. For the Kerr black hole with spin a∗ ≃ 0.9982 the characteristic “humpy frequency” and the radial epicyclic frequency at the orbit, where the positive rate of change of the LNRF-related orbital velocity with the proper radial distance is maxi mal, are in ratio 1:3. Identifying the radial epicyclic frequency with the ob served 250 Hz QPO, we arrive at the mass of the black hole. In this method the ratio of frequencies determines the spin (and vice versa), and concrete values of frequencies determine the black-hole mass. Results. Mass of the Kerr black hole in XTE J1650-500 binary system is estimated to be around 5.1 M⊙.

LNRF-velocity hump-induced oscillations of a Keplerian disc orbiting near-extreme Kerr black hole: a possible explanation of high-frequency QPOs in GRS 1915+105

Context.At least four high-frequency quasiperiodic oscillations (QPOs) at frequencies 41 Hz, 67 Hz, 113 Hz, and 167 Hz were reported in a binary system GRS 1915+105 hosting near-extreme Kerr black hole with a dimensionless spin .

Iron Fluorescence from within the Innermost Stable Orbit of Black Hole Accretion Disks

The fluorescent iron Kα line is a powerful observational probe of the inner regions of black hole accretion disks. Previous studies have assumed that only material outside the radius of marginal stability (r = 6m for a Schwarzschild hole) can contribute to the observed line emission. Here we show that fluorescence by material inside the radius of marginal stability, which is in the process of spiraling toward the event horizon, can have an observable influence on the iron line profile and equivalent width. For concreteness, we consider the case of a geometrically thin accretion disk, around a Schwarzschild black hole, in which fluorescence is excited by an X-ray source placed at some height above the disk and on the axis of the disk. Fully relativistic line profiles are presented for various source heights and efficiencies. It is found that the extra line flux generally emerges in the extreme red wing of the iron line, because of the large gravitational redshift experienced by photons from the region within the radius of marginal stability. We apply our models to the variable iron line seen in the ASCA spectrum of the Seyfert nucleus MCG -6-30-15. It is found that the change in the line profile, equivalent width, and continuum normalization can be well explained as being due to a change in the height of the source above the disk. Thus, we can explain the iron line properties of MCG -6-30-15 within the context of an accretion disk around a nonrotating black hole. This contrasts with previous studies that, due to the absence of fluorescence from within the radius of marginal stability, have indicated that this object possesses a rapidly rotating (i.e., near-extremal Kerr) black hole. This is an important issue since it has a direct bearing on the spin paradigm for the radio-loud/radio-quiet dichotomy seen in accreting black hole systems. We discuss some future observational tests that could help distinguish slowly rotating black holes from rapidly rotating holes.