Narrow Results

Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of Kerr and extremal Kerr black holes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the Kerr and extremal Kerr black holes. The real part of the quasinormal frequencies of Kerr black hole used for this computation is of the form mΩ where Ω is the angular velocity of the black hole horizon. The resulting spectrum is discrete but not as expected uniformly spaced. Thus, we infer that the function describing the real part of quasinormal frequencies of Kerr black hole is not the correct one. This conclusion is in agreement with the numerical results for the highly damped quasinormal modes of Kerr black hole recently presented by Berti, Cardoso and Yoshida. On the contrary, extremal Kerr black hole is shown to have a discrete area spectrum which in addition is evenly spaced. The area spacing derived in our analysis for the extremal Kerr black hole area spectrum is not proportional to ln 3. Therefore, it does not give support to Hod's statement that the area spectrum should be valid for a generic Kerr–Newman black hole.

Using the Hamilton–Jacobi method, we discuss the Hawking radiation of the Kerr black hole. The result shows when the self-gravitational interaction as well as the conservation of energy and angular momentum are taken into account, the radiation spectrum deviates from the purely thermal one and the tunneling probability is related to the change of Bekenstein–Hawking entropy, which is in accordance with Parikh and Wilczek's result and gives a method to study the Hawking radiation of the black hole.

We find linearly independent solutions of the Goncharov–Firsova equation in the case of a massive complex scalar field on a Kerr black hole. The solutions generalize, in some sense, the classical monopole spherical harmonic solutions previously studied in the massless cases.

Previously we investigated classical motion of a string in (3+1)-dimensional spherically symmetric neutral and charged black holes. As an extension the solutions in (3+1)-dimensional axially symmetric rotating black hole are investigated. The solutions for the wiggly string exhibit open strings lying in the radial direction in the equatorial plane outside the horizon.

In the presence of a rotating Kerr black hole, we investigate hydrodynamics of the massive particles and massless photons to construct relations among number density, pressure and internal energy density of the massive particles and photons around the rotating Kerr black hole and to study an accretion onto the black hole. On equatorial plane of the Kerr black hole, we investigate the bound orbits of the massive particles and photons around the black hole to produce their radial, azimuthal and precession frequencies. With these frequencies, we study the black holes GRO J1655-40 and 4U 1543-47 to explicitly obtain the radial, azimuthal and precession frequencies of the massive particles in the flow of perfect fluid. We next consider the massive particles in the stable circular orbit of radius of 1.0 ly around the supernovas SN 1979C, SN 1987A and SN 2213-1745 in the Kerr curved spacetime, and around the potential supermassive Schwarzschild black holes M87, NGC 3115, NGC 4594, NGC 3377, NGC 4258, M31, M32 and Galatic center, to estimate their radial and azimuthal frequencies, which are shown to be the same results as those in no precession motion. The photon unstable orbit is also discussed in terms of the impact parameter of the photon trajectory. Finally, on the equatorial plane of the Kerr black hole, we construct the global flat embedding structures possessing (9 + 3) dimensionalities outside and inside the event horizon of the rotating Kerr black hole. Moreover, on the plane, we investigate the warp products of the Kerr spacetime.

In this paper, a matrix method is employed to study the scalar quasinormal modes of Kerr as well as Kerr–Sen black holes. Discretization is applied to transfer the scalar perturbation equation into a matrix form eigenvalue problem, where the resulting radial and angular equations are derived by the method of separation of variables. The eigenvalues, quasinormal frequencies $\omega$ and angular quantum numbers $\lambda$, are then obtained by numerically solving the resultant homogeneous matrix equation. This work shows that the present approach is an accurate, as well as efficient method for investigating quasinormal modes.

We calculate thermal corrections to the Casimir energy of a massless scalar field in the Kerr black hole surrounded by quintessence, taking into account the metrics derived by Ghosh [S. G. Ghosh, Eur. Phys. J. C76, 222 (2016)] and Toshmatov et al. [B. Toshmatov, Z. Stuchlík and B. Ahmedov, Eur. Phys. J. Plus132, 98 (2017)]. We compare both results and show that they are almost the same, except very close to the horizons. At $𝜃=\pi /2$, equatorial plane, the results are the same, as should be expected, due to the fact that the metrics coincide in this region.

The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and Stojkovic. We also show that five-dimensional AdS Kerr black holes are isospectrum deformations of Ricci-flat Kerr black holes in the sense that the eigenvalues of the Weyl curvature are preserved.

The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL(2, ℝ) × U(1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.

We investigate some of the quantum gravity effects on a vacuum created pair of -brane by a nonlinear U(1) gauge theory on a D₄-brane. In particular, we obtain a four-dimensional quantum Kerr–(Newman) black hole in an effective torsion curvature formalism sourced by a two form dynamics in the worldvolume of a D₄-brane on S¹. Interestingly, the event horizon is found to be independent of a nonlinear electric charge and the 4D quantum black hole is shown to describe degenerate vacua in string theory. We show that the quantum Kerr brane universe possesses its origin in a de Sitter vacuum. In a nearly S₂-symmetric limit, the Kerr geometries may seen to describe a Schwarzschild and Reissner–Nordstrom quantum black holes. It is argued that a quantum Reissner–Nordstrom tunnels to a large class of degenerate Schwarzschild vacua. In a low energy limit, the nonlinear electric charge becomes significant at the expense of the degeneracies. In the limit, the quantum geometries may identify with the semiclassical black holes established in Einstein gravity. Analysis reveals that a quantum geometry on a vacuum created D₃-brane universe may be described by a low energy perturbative string vacuum in presence of a nonperturbative quantum correction.

In this paper, a Kerr-type solution in the Regge calculus is considered. It is assumed that the discrete general relativity, the Regge calculus, is quantized within the path integral approach. The only consequence of this approach used here is the existence of a length scale at which edge lengths are loosely fixed, as considered in our earlier paper. In addition, we previously considered the Regge action on a simplicial manifold on which the vertices are coordinatized and the corresponding piecewise constant metric is introduced, and found that for the simplest periodic simplicial structure and in the leading order over metric variations between four-simplices, this reduces to a finite-difference form of the Hilbert–Einstein action. The problem of solving the corresponding discrete Einstein equations (classical) with a length scale (having a quantum nature) arises as the problem of determining the optimal background metric for the perturbative expansion generated by the functional integral. Using a one-complex-function ansatz for the metric, which reduces to the Kerr–Schild metric in the continuum, we find a discrete metric that approximates the continuum one at large distances and is nonsingular on the (earlier) singularity ring. The effective curvature $R_{\lambda \nu \nu \rho }$, including where $R_{\lambda \mu }\ne 0$ (gravity sources), is analyzed with a focus on the vicinity of the singularity ring.

A new exact time-dependent Kerr-like black hole solution is found on a Randall–Sundrum brane world spacetime. The solution is also valid on the Wick-rotated Euclidean counterpart space, so represents equally well a gravitational instanton, i.e. a bump in spacetime. Since the r-dependent part is determined by a first-order differential equation, one conjectures that the solution is a self-dual solution comparable with the Eguchi–Hanson solution. The zeroes and poles of the spacetime are determined by a quintic polynomial. To describe the Hawking particles, one uses the antipodal boundary condition on a complex Klein-bottle hypersurface ${ℂ}^1\times {ℂ}^1$. We used the Hopf fibration to get $S^2$ as the black hole horizon, where the centrix is not in a torus but in the Klein bottle. The twist fits very well with the antipodal identification of the point on the horizon. No “cut-and-paste” is necessary, so the Hawing particles remain pure without instantaneous information transport. A local observer passing the horizon will not notice a central singularity in suitable coordinates. The black hole paradoxes are also revisited in our new black hole model. A connection is made with the geometric quantization of ${ℂ}^1\times {ℂ}^1\sim S^3$, by considering the symplectic 2-form. The model can be easily extended to the non-vacuum situation by including a scalar field. Both the dilaton and the scalar field can be treated as quantum fields when approaching the Planck area.

Taking into account the generalized uncertainty principle (GUP), we calculate the entropy of a scalar field in a Kerr spacetime. Different to previous work, we have used an new equation of the density of quantum states, which arises from the modified commutation relation . The divergence in the brick wall model is removed, without the cutoff.

In the present study, we perform the numerical simulation of a relativistic thin accretion disk around the nonrotating and rapidly rotating black holes using the general relativistic hydrodynamic code with Kerr in Kerr–Schild coordinate that describes the central rotating black hole. Since the high energy X-rays are produced close to the event horizon resulting the black hole–disk interaction, this interaction should be modeled in the relativistic region.

We have set up two different initial conditions depending on the values of thermodynamical variables around the black hole. In the first setup, the computational domain is filled with constant parameters without injecting gas from the outer boundary. In the second, the computational domain is filled with the matter which is then injected from the outer boundary. The matter is assumed to be at rest far from the black hole. Both cases are modeled over a wide range of initial parameters such as the black hole angular momentum, adiabatic index, Mach number and asymptotic velocity of the fluid. It has been found that initial values and setups play an important role in determining the types of the shock cone and in designating the events on the accretion disk. The continuing injection from the outer boundary presents a tail shock to the steady state accretion disk. The opening angle of shock cone grows as long as the rotation parameter becomes larger. A more compressible fluid (bigger adiabatic index) also presents a bigger opening angle, a spherical shock around the rotating black hole, and less accumulated gas in the computational domain. While results from [J. A. Font, J. M. A. Ibanez and P. Papadopoulos, Mon. Not. R. Astron. Soc.305 (1999) 920] indicate that the tail shock is warped around for the rotating hole, our study shows that it is the case not only for the warped tail shock but also for the spherical and elliptical shocks around the rotating black hole. The warping around the rotating black hole in our case is much smaller than the one by [J. A. Font, J. M. A. Ibanez and P. Papadopoulos, Mon. Not. R. Astron. Soc.305 (1999) 920], due to the representation of results at the different coordinates. Contrary to the nonrotating black hole, the tail shock is slightly warped around the rotating black hole. The filled computational domain without any injection leads to an unstable accretion disk. However much of it reaches a steady state for a short period of time and presents quasi-periodic oscillation (QPO). Furthermore, the disk tends to loose mass during the whole dynamical evolution. The time-variability of these types of accretion flowing close to the black hole may clarify the light curves in Sgr A*.

We report exotic orbital phenomena of spinning test particles orbiting around a Kerr black hole, i.e. some orbits of spinning particles are asymmetrical about the equatorial plane. When a nonspinning test particle orbits around a Kerr black hole in a strong field region, due to relativistic orbital precessions, the pattern of trajectories is symmetrical about the equatorial plane of the Kerr black hole. However, the patterns of the spinning particles’ orbit are no longer symmetrical about the equatorial plane for some orbital configurations and large spins. We argue that these asymmetrical patterns come from the spin–spin interactions between spinning particles and Kerr black holes, because the directions of spin–spin forces can be arbitrary, and distribute asymmetrically about the equatorial plane.

Recently (Int. J. Mod. Phys. D 27 (2018) 1847025) an interesting property of closed light rings in Kerr black holes has been noticed. We explain its origin and derive a slightly more general result.

In this paper, we compute the black hole entropy and the entanglement entropy of Hawking radiations due to photons during the evaporation of a 4D asymptotically flat Kerr black hole. The Page curve for the Kerr black hole is obtained in the original way à la Page, and it qualitatively mimics the curve for the Schwarzschild black hole but has some new features.

We present a generalization of previous results regarding the stability under gravitational perturbations of nakedly singular super extreme Kerr spacetime and Kerr black hole interior beyond the Cauchy horizon. To do so we study solutions to the radial and angular Teukolsky's equations with different spin weights, particulary s = ±1 representing electromagnetic perturbations, s = ±1/2 representing a perturbation by a Dirac field and s = 0 representing perturbations by a scalar field. By analizing the properties of radial and angular eigenvalues we prove the existence of an infinite family of unstable modes.

This paper applies the first-order Seiberg–Witten map to evaluate the first-order non-commutative Kerr tetrad. The classical tetrad is taken to follow the locally non-rotating frame prescription. We also evaluate the tiny effect of non-commutativity on the efficiency of the Penrose process of rotational energy extraction from a black hole.

In this paper, we analyze the modification to the thermodynamics of a Schwarzschild black hole and a Kerr black hole due to gravity’s rainbow. The metric for these black holes will be made energy dependent. This will be done by using rainbow functions motivated from the hard spectra from gamma-ray bursters at cosmological distances. This modification of the metric by these rainbow functions will in turn modify the temperature and entropy of these black holes. We will also discuss how this affects the formation of virtual black holes.