Angular Momentum Of Black Hole Research Articles

Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit

In the present work we study numerically quasiequatorial lensing by the charged, stationary, axially symmetric Kerr-Sen dilaton-axion black hole in the strong deflection limit. In this approximation we compute the magnification and the positions of the relativistic images. The most outstanding effect is that the Kerr-Sen black hole caustics drift away from the optical axis and shift in the clockwise direction with respect to the Kerr caustics. The intersections of the critical curves on the equatorial plane as a function of the black hole angular momentum are found, and it is shown that they decrease with the increase of the parameter ${Q}^{2}/M$. All of the lensing quantities are compared to particular cases as Schwarzschild, Kerr, and Gibbons-Maeda black holes.

X‐ray spectra and polarization from accreting black holes: polarization from an orbiting spot

AbstractThe polarization from a spot orbiting around Schwarzschild and extreme Kerr black holes is studied. We assume different models of local polarization. Firstly, as a toy model we set the local polarization vector either normal to the disc plane, or perpendicular to the toroidal magnetic field. Then we examine the more realistic situation with a spot arising due to the emission from the primary source above the disc. We employ either Rayleigh single scattering or Compton multiple scattering approximations. The time dependence of the degree and angle of polarization during the spot revolution is examined as a function of the observer's inclination angle and black hole angular momentum. The gravitational and Doppler shifts, lensing effect as well as time delays are taken into account. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Quasinormal ringing of Kerr black holes: The excitation factors

Distorted black holes radiate gravitational waves. In the so-called ringdown phase radiation is emitted in a discrete set of complex quasinormal frequencies, whose values depend only on the black hole's mass and angular momentum. Ringdown radiation could be detectable with large signal-to-noise ratio by the Laser Interferometer Space Antenna LISA. If more than one mode is detected, tests of the black hole nature of the source become possible. The detectability of different modes depends on their relative excitation, which in turn depends on the cause of the perturbation (i.e. on the initial data). A ``universal'', initial data-independent measure of the relative mode excitation is encoded in the poles of the Green's function that propagates small perturbations of the geometry (``excitation factors''). We compute for the first time the excitation factors for general-spin perturbations of Kerr black holes. We find that for corotating modes with $l=m$ the excitation factors tend to zero in the extremal limit, and that the contribution of the overtones should be more significant when the black hole is fast rotating. We also present the first analytical calculation of the large-damping asymptotics of the excitation factors for static black holes, including the Schwarzschild and Reissner-Nordstrom metrics. This is an important step to determine the convergence properties of the quasinormal mode expansion.

Unitarity in the presence of closed timelike curves

We conjecture that, in certain cases, quantum dynamics is consistent in the presence of closed timelike curves. We consider time dependent orbifolds of three dimensional Minkowski space describing, in the limit of large AdS radius, BTZ black holes inside the horizon. Although perturbative unitarity fails, we show that, for discrete values of the gravitational coupling, particle propagation is consistent with unitarity. This quantization corresponds to the quantization of the black hole angular momentum, as expected from the dual CFT description. Note, however, that we recover this result by analyzing the physics inside the horizon and near the singularity. The spacetime under consideration has no AdS boundary, and we are therefore not using any assumption regarding a possible dual formulation. We perform the computation at very low energies, where string effects are irrelevant and interactions are dominated by graviton exchange in the eikonal regime. We probe the non-causal structure of space-time to leading order, but work to all orders in the gravitational coupling.

Quasinormal modes of brane-localized standard model fields. II. Kerr black holes

This paper presents a comprehensive study of the fundamental quasinormal modes of all standard model fields propagating on a brane embedded in a higher-dimensional rotating black-hole spacetime. The equations of motion for fields with spin $s=0$, $1/2$ and 1 propagating in the induced-on-the-brane background are solved numerically, and the dependence of their QN spectra on the black-hole angular momentum and dimensionality of spacetime is investigated. It is found that the brane-localized field perturbations are longer-lived when the higher-dimensional black hole rotates faster, while an increase in the number of transverse-to-the-brane dimensions reduces their lifetime. Finally, the quality factor $Q$, that determines the best oscillator among the different field perturbations, is investigated and found to depend on properties of both the particular field studied (spin, multipole numbers) and the gravitational background (dimensionality, black-hole angular momentum parameter).

Polarization from an orbiting spot

AbstractThe polarization from a spot orbiting around Schwarzschild and extreme Kerr black holes is studied. The time dependence of the degree and angle of polarization during the spot revolution is examined as a function of the observer's inclination angle and black hole angular momentum. The gravitational and Doppler shifts, lensing effect as well as time delays are taken into account.

Introduction to dynamical horizons in numerical relativity

This paper presents a quasilocal method of studying the physics of dynamical black holes in numerical simulations. This is done within the dynamical horizon framework, which extends the earlier work on isolated horizons to time-dependent situations. In particular: (i) We locate various kinds of marginal surfaces and study their time evolution. An important ingredient is the calculation of the signature of the horizon, which can be either spacelike, timelike, or null. (ii) We generalize the calculation of the black hole mass and angular momentum, which were previously defined for axisymmetric isolated horizons to dynamical situations. (iii) We calculate the source multipole moments of the black hole which can be used to verify that the black hole settles down to a Kerr solution. (iv) We also study the fluxes of energy crossing the horizon, which describes how a black hole grows as it accretes matter and/or radiation. We describe our numerical implementation of these concepts and apply them to three specific test cases, namely, the axisymmetric head-on collision of two black holes, the axisymmetric collapse of a neutron star, and a nonaxisymmetric black hole collision with nonzero initial orbital angular momentum.

Rotating black holes at future colliders. III. Determination of black hole evolution

TeV scale gravity scenario predicts that the black hole production dominates over all other interactions above the scale and that the Large Hadron Collider will be a black hole factory. Such higher dimensional black holes mainly decay into the standard model fields via the Hawking radiation whose spectrum can be computed from the greybody factor. Here we complete the series of our work by showing the greybody factors and the resultant spectra for the brane localized spinor and vector field emissions for arbitrary frequencies. Combining these results with the previous works, we determine the complete radiation spectra and the subsequent time evolution of the black hole. We find that, for a typical event, well more than half a black hole mass is emitted when the hole is still highly rotating, confirming our previous claim that it is important to take into account the angular momentum of black holes.

Production of black holes and their angular momentum distribution in models with split fermions

In models with TeV-scale gravity it is expected that mini black holes will be produced in near-future accelerators. On the other hand, TeV-scale gravity is plagued with many problems like fast proton decay, unacceptably large neutron-antineutron oscillations, flavor changing neutral currents, large mixing between leptons, etc. Most of these problems can be solved if different fermions are localized at different points in the extra dimensions. We study the cross-section for the production of black holes and their angular momentum distribution in these models with "split" fermions. We find that, for a fixed value of the fundamental mass scale, the total production cross section is reduced compared with models where all the fermions are localized at the same point in the extra dimensions. Fermion splitting also implies that the bulk component of the black hole angular momentum must be taken into account in studies of the black hole decay via Hawking radiation.

Studies of accretion flows around rotating black holes - I. Particle dynamics in a pseudo-Kerr potential

In thisseries of papers, we shall present a simplistic approach to the study of particle dynamics, fluid dynamics and numerical simulations of accretion flows and outflows around rotating black holes. We show that with a suitably modified effective potential of the central gravitating rotating object, one can carry out these studies very accurately. In this approach, one need not use the full general relativistic equations to obtain the salient features of the general relativistic flows provided the Kerr parameter remains within -1 ≤ a ≤ 0.8. We present the equatorial and the non-equatorial particle trajectories from our potential and compare salient properties in Kerr and in pseudo-Kerr geometries. Our potential naturally produces accurate results for motions around the Schwarzschild geometry when the black hole angular momentum is set to zero.

Erratum: Entropy of a Kerr-de Sitter black hole due to arbitrary spin fields [Phys. Rev. D69, 044019 (2004)

The Newman-Penrose formalism is used to derive the Teukolsky master equations controlling massless scalar, neutrino, electromagnetic, gravitino, and gravitational field perturbations of the Kerr-de Sitter spacetime. Then the quantum entropy of a non-extreme Kerr-de Sitter black hole due to arbitrary spin fields is calculated by the improved thin-layer brick wall model. It is shown that the subleading order contribution to the entropy is dependent on the square of the spins of particles and that of the specific angular momentum of black holes as well as the cosmological constant. The logarithmic correction of the spins of particles to the entropy relies on the rotation of the black hole and the effect of the cosmological constant.

Unitarity in the presence of closed timelike curves

AbstractWe conjecture that, in certain cases, quantum dynamics is consistent in the presence of closed timelike curves. We consider time dependent orbifolds of three dimensional Minkowski space describing, in the limit of large AdS radius, BTZ black holes inside the horizon. Although perturbative unitarity fails, we show that, for discrete values of the gravitational coupling, particle propagation is consistent with unitarity. This quantization corresponds to the quantization of the black hole angular momentum. We perform the computation at very low energies, where string effects are irrelevant and interactions are dominated by graviton exchange in the eikonal regime.

Unitarity with Closed Timelike Curves

We conjecture that, in certain cases, quantum dynamics is consistent in the presence of closed timelike curves. We consider time dependent orbifolds of three dimensional Minkowski space describing, in the limit of large AdS radius, BTZ black holes inside the horizon. Although perturbative unitarity fails, we show that, for discrete values of the gravitational coupling, particle propagation is consistent with unitarity. This quantization corresponds to the quantization of the black hole angular momentum. We perform the computation at very low energies, where string effects are irrelevant and interactions are dominated by graviton exchange in the eikonal regime.

Oscillation modes of relativistic slender tori

Accretion flows with pressure gradients permit the existence of standing waves which may be responsible for observed quasi-periodic oscillations (QPO's) in X-ray binaries. We present a comprehensive treatment of the linear modes of a hydrodynamic, non-self-gravitating, polytropic slender torus, with arbitrary specific angular momentum distribution, orbiting in an arbitrary axisymmetric space-time with reflection symmetry. We discuss the physical nature of the modes, present general analytic expressions and illustrations for those which are low order, and show that they can be excited in numerical simulations of relativistic tori. The mode oscillation spectrum simplifies dramatically for near Keplerian angular momentum distributions, which appear to be generic in global simulations of the magnetorotational instability. We discuss our results in light of observations of high frequency QPO's, and point out the existence of a new pair of modes which can be in an approximate 3:2 ratio for arbitrary black hole spins and angular momentum distributions, provided the torus is radiation pressure dominated. This mode pair consists of the axisymmetric vertical epicyclic mode and the lowest order axisymmetric breathing mode.

Black-hole ringdown search in TAMA300: matched filtering and event selections

Detecting gravitational ringdown waves provides a probe for direct observation of astrophysical black holes. The masses and angular momenta of black holes can be determined from the waveforms by using the black-hole perturbation theory. In this paper we present data analysis methods to search for black-hole ringdowns of fundamental quasi-normal modes with interferometric gravitational wave detectors, and report an application to the TAMA300 data. Our method is based upon matched filtering by which we calculate cross-correlations between detector outputs and reference waveforms. In a search for gravitational signals, fake reductions and event identifications are of most importance. We developed two methods to reject spurious triggers in filter outputs in the time domain and examined their reduction powers. It is shown that by using the methods presented here the number of fake triggers can be reduced by an order with a false dismissal probability of 5%. We also discuss the possibility of using the higher order quasi-normal modes for event selection.

Angular momentum of massive black holes

The origin of the angular momentum of objects, resulting from gravitational collapse, is discussed. It is shown that origin of the spins of the bodies comprised of baryon matter can be explained by the tidal forces acting from the neighbors during gravitational collapse. We discuss also the problem of origin of an angular momentum of a black hole. The masses of black holes in the center of galaxies must have the lower limit M > 10 6 M ⊙ if they originate from the accretion of baryon matter on them. We suggest to estimate the angular momentum of massive black holes by measuring the radii of jets near their bases on the accretion disks around the black holes.

Measuring mass and angular momentum of black holes with high-frequency quasi-periodic oscillations

For the three microquasars GRO J1655-40, XTE J1550-564 and GRS 1915+105 twin high frequency quasi-periodic oscillations (HFQPOs) with a ratio of 3:2 and/or 3:1 have been measured. For a test particle orbiting a rotating black hole on a stable circular orbit there exist two different orbits at which the vertical and radial epicyclic oscillations are in either a 3:1 or 3:2 parametric resonance for any choice of the black hole angular momentum a. If the two orbits are required to be frequency commensurable Keplerian orbits there is only one solution for the two orbit radii and a. This model predicts that the microquasars have the same a, and it predicts their black hole masses on the basis of the measured HFQPOs in agreement with the dynamically determined masses. Application of this model to the Galactic Center black hole Sgr A* using the recently measured QPOs (Genzel et al. [CITE]; Aschenbach et al. [CITE]) leads to a black hole mass of , and the same a as for the microquasars. The possibility that all four sources have suggests that this value is the upper limit of a imposed by general relativity. The same value for the lower orbit radius and the same value for a are also suggested by an analysis of the general relativistic expression for the radial gradient of the orbital velocity, which changes sign in a narrow annular region around the lower orbit when .

Multitemperature Blackbody Spectra of Thin Accretion Disks with and without a Zero‐Torque Inner Boundary Condition

The standard spectral model for analyzing the soft component of thermal emission from a thin accretion disk around a black hole is the multitemperature blackbody model. The widely used implementation of this model, which is known as diskbb, assumes nonzero torque at the inner edge of the accretion disk. This assumption is contrary to the classic and current literature on thin-disk accretion, which advocates the use of a zero-torque boundary condition. Consequently, we have written code for a zero-torque model, ezdiskbb, which we compare to the nonzero-torque model diskbb by fitting Rossi X-Ray Timing Explorer spectra of three well-known black hole binaries: 4U 1543-47, XTE J1550-564, and GRO J1655-40. The chief difference we find is that the zero-torque model gives a value for the inner disk radius that is ≈2.2 times smaller than the value given by diskbb. This result has important implications, especially for the determination of black hole angular momentum and mass accretion rate.

Interpreting the High‐Frequency Quasi‐periodic Oscillation Power Spectra of Accreting Black Holes

In the context of a relativistic hot spot model, we investigate different physical mechanisms to explain the behavior of quasi-periodic oscillations (QPOs) from accreting black holes. The locations and amplitudes of the QPO peaks are determined by the calculations presented previously by Schnittman & Bertschinger: the black hole mass and angular momentum give the geodesic coordinate frequencies, while the disk inclination and the hot spot size, shape, and overbrightness give the amplitudes of the different peaks. In this paper additional features are added to the existing model to explain the broadening of the QPO peaks as well as the damping of higher frequency harmonics in the power spectrum. We present a number of analytic results that closely agree with more-detailed numerical calculations. Three primary pieces are developed: the addition of multiple hot spots with random phases, a finite width in the distribution of geodesic orbits, and the scattering of photons from the hot spot through a corona of hot electrons around the black hole. Finally, the complete model is used to fit the observed power spectra of both type A and type B QPOs seen in XTE J1550-564, giving confidence limits on each of the model parameters.

The Harmonic Structure of High‐Frequency Quasi‐periodic Oscillations in Accreting Black Holes

Observations from the Rossi X-Ray Timing Explorer have shown the existence of high-frequency quasi-periodic oscillations (HFQPOs) in the X-ray flux from accreting black hole binary systems. In at least two systems, these HFQPOs come in pairs with a 2 : 3 frequency commensurability. We employ a simple model to explain the position and amplitude of the HFQPO peaks. Using the exact geodesic equations for the Kerr metric, we calculate the trajectories of massive test particles, which are treated as isotropic, monochromatic emitters in their rest frames. Photons are traced from the accretion disk to a distant observer to produce time- and frequency-dependent images of the orbiting hot spot and background disk. The power spectrum of the X-ray light curve consists of multiple peaks at integral combinations of the black hole coordinate frequencies. In particular, if the radial frequency is one-third of the azimuthal frequency (as is the case near the innermost stable circular orbit), beat frequencies appear in the power spectrum at two-thirds and four-thirds of the fundamental azimuthal orbital frequency, in agreement with observations. In addition, we model the effects of shearing the hot spot in the disk, producing an arc of emission that also follows a geodesic orbit, as well as the effects of nonplanar orbits that experience Lens-Thirring precession around the black hole axis. By varying the arc length, we are able to explain the relative amplitudes of the QPOs at either 2ν or 3ν in observations from XTE J1550-564 and GRO J1655-40. In the context of this model, the observed power spectra allow us to infer values for the black hole mass and angular momentum and also constrain the parameters of the model, such as the hot spot size and luminosity.