Energy and angular momentum flow into a black hole

The area of the event horizon round a rotating black hole will increase in the presence of a non-axisymmetric or time dependent perturbation. If the perturbation is a matter field, the area increase is related to the fluxes of energy and of angular momentum into the black hole in such a way as to maintain the formula for the area in the Kerr solution. For purely gravitational perturbations one cannot define angular momentum locally but one can use the area increase and the expression for area in terms of mass and angular momentum to calculate the slowing down of a black hole caused by a non-axisymmetric distribution of matter at a distance. It seems that the coupling between the rotation of a black hole and the orbit of a particle going round it can be significant if the angular momentum of the black hole is close to its maximum possible value and if the angular velocity of the particle is nearly equal to that of the black hole.Alfred P. Sloan Research Fellow, supported in part by the National Science Foundation.     

Novel Rotating Hairy Black Hole in （2 ＋ 1） Dimensions

We present some novel rotating hairy black hole metric in （2 ＋ 1） dimensions, which is an exact solution to the field equations of the Einstein-scalar-AdS theory with a non-minimal coupling. The scalar potential is determined by the metric ansatz and consistency of the field equations and cannot be prescribed arbitrarily. In the simplified, critical ease, the scalar potential contains two independent constant parameters, which are respectively related to the mass and angular momentum of the black hole in a particular way. As long as the angular momentum does not vanish, the metric can have zero, one or two horizons. The case with no horizon is physically uninteresting because of the curvature singularity lying at the origin. We identify the necessary conditions for at least one horizon to be present in the solution, which imposes some bound on the mass-angular momentum ratio. For some particular choice of pararneters our solution degenerates into some previously known black hole solutions.     

A rotating black ring solution in five dimensions

The vacuum Einstein equations in five dimensions are shown to admit a solution describing a stationary asymptotically flat spacetime regular on and outside an event horizon of topology S1xS2. It describes a rotating "black ring." This is the first example of a stationary asymptotically flat vacuum solution with an event horizon of nonspherical topology. The existence of this solution implies that the uniqueness theorems valid in four dimensions do not have simple five-dimensional generalizations. It is suggested that increasing the spin of a spherical black hole beyond a critical value results in a transition to a black ring, which can have an arbitrarily large angular momentum for a given mass.     

Particle acceleration in Horava–Lifshitz black holes

In this paper we calculate the center-of-mass energy of two colliding test particles near the rotating and non-rotating Horava–Lifshitz black hole. For the case of a slowly rotating KS solution of Horava–Lifshitz black hole we compare our results with the case of Kerr black holes. We confirm the limited value of the center-of-mass energy for static black holes and unlimited value of the center-of-mass energy for rotating black holes. Numerically, we discuss temperature dependence of the center-of-mass energy on the black hole horizon. We obtain the critical angular momentum of particles. In this limit the center-of-mass energy of two colliding particles in the neighborhood of the rotating Horava–Lifshitz black hole could be arbitrarily high. We found appropriate conditions where the critical angular momentum could have an orbit outside the horizon. Finally, we obtain the center-of-mass energy corresponding to this circle orbit.     

Cold plasma dispersion relations in the vicinity of a Schwarzschild black hole horizon

We apply the ADM 3 + 1 formalism to derive the general relativistic magnetohydrodynamic equations for cold plasma in spatially flat Schwarzschild metric. Respective perturbed equations are linearized for non-magnetized and magnetized plasmas both in non-rotating and rotating backgrounds. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed for the existence of waves with positive angular frequency in the region near the horizon. Our results support the fact that no information can be extracted from the Schwarzschild black hole. It is concluded that negative phase velocity propagates in the rotating background whether the black hole is rotating or non-rotating.     

The collisional Penrose process

Shortly after the discovery of the Kerr metric in 1963, it was realized that a region existed outside of the black hole’s event horizon where no time-like observer could remain stationary. In 1969, Roger Penrose showed that particles within this ergosphere region could possess negative energy, as measured by an observer at infinity. When captured by the horizon, these negative energy particles essentially extract mass and angular momentum from the black hole. While the decay of a single particle within the ergosphere is not a particularly efficient means of energy extraction, the collision of multiple particles can reach arbitrarily high center-of-mass energy in the limit of extremal black hole spin. The resulting particles can escape with high efficiency, potentially serving as a probe of high-energy particle physics as well as general relativity. In this paper, we briefly review the history of the field and highlight a specific astrophysical application of the collisional Penrose process: the potential to enhance annihilation of dark matter particles in the vicinity of a supermassive black hole.     

Collision of spinning particles near BTZ black holes

We study the collision property of spinning particles near a Ba?ados-Teitelboim-Zanelli(BTZ)black hole.Our results show that although the center-of-mass energy of two ingoing particles diverges if one of the particles possesses a critical angular momentum,the particle with critical angular momentum cannot exist outside of the horizon due to violation of the timelike constraint.Further detailed investigation indicates that only a particle with a subcritical angular momentum is allowed to exist near an extremal rotating BTZ black hole,and the corresponding collision center-of-mass energy can be arbitrarily large in a critical angular momentum limit.     

ROTATING RINDLER SPACE TIME WITH CONSTANT ANGULAR VELOCITY

A new space time metric is derived from Kerr metric if its mass and location approach to infinite in an appropriate way. The new space-time is an infinitesimal neighborhood nearby one of the two horizon poles of an infinite Kerr black hole. In other words, it is the second order infinitesimal neighborhood nearby one of the two horizon poles of a Kerr black hole. It is flat and has event horizon and infinite red shift surface. We prove that it is a rotating Rindler space time with constant angular velocity.     

Binary-black-hole encounters, gravitational bursts, and maximum final spin

The spin of the final black hole in the coalescence of nonspinning black holes is determined by the "residual" orbital angular momentum of the binary. This residual momentum consists of the orbital angular momentum that the binary is not able to shed in the process of merging. We study the angular momentum radiated, the spin of the final black hole, and the gravitational bursts in a sequence of equal mass encounters. The initial orbital configurations range from those producing an almost direct infall to others leading to numerous orbits before infall, with multiple bursts of radiation. Our sequence consists of orbits with fixed impact parameter. What varies is the initial linear momentum of the black holes. For this sequence, the final black hole of mass M_{h} gets a maximum spin parameter a/M_{h} approximately 0.823, with this maximum occurring for initial orbital angular momentum L/M_{h};{2} approximately 1.176.     

Metric of a tidally distorted nonrotating black hole

The metric of a tidally distorted, nonrotating black hole is presented in a light-cone coordinate system that penetrates the event horizon and possesses a clear geometrical meaning. The metric is expressed as an expansion in powers of r/R<1, where r is a measure of distance from the black hole and R is the local radius of curvature of the external spacetime; this is assumed to be much larger than M, the mass of the black hole. The metric is calculated up to a remainder of order (r/R)4, and it depends on a family of tidal gravitational fields which characterize the hole's local environment. The coordinate system allows an easy identification of the event horizon, and expressions are derived for its surface gravity and the rates at which the tidal interaction transfers mass and angular momentum to the black hole.     

From Schwarzschild to Kerr due to Black Hole Quantum Tunnelling

Hawking radiation can be viewed as a process of quantum tunnelling near black hole horizon. When a particle with angular momentum tunnels across the event horizon of Schwarzschild black hole, the black hole will change into a Kerr black hole. The emission rate of the massless particles with angular momentum is calculated, and the result is consistent with an underlying unitary theory.     

Dynamics of particles around a pseudo-Newtonian Kerr black hole with halos

The regular and chaotic dynamics of test particles in a superposed field between a pseudo-Newtonian Kerr black hole and quadrupolar halos is detailed.In particular,the dependence of dynamics on the quadrupolar parameter of the halos and the spin angular momentum of the rotating black hole is studied.It is found that the small quadrupolar moment,in contrast with the spin angular momentum,does not have a great effect on the stability and radii of the innermost stable circular orbits of these test particles.In addition,chaos mainly occurs for small absolute values of the rotating parameters,and does not exist for the maximum counter-rotating case under some certain initial conditions and parameters.This means that the rotating parameters of the black hole weaken the chaotic properties.It is also found that the counter-rotating system is more unstable than the co-rotating one.Furthermore,chaos is absent for small absolute values of the quadrupoles,and the onset of chaos is easier for the prolate halos than for the oblate ones.     

Asymptotic level density in heterotic string theory and rotating black holes

We calculate the density of states with given mass and spin in string theory and obtain asymptotic formulas. We also compute the tree-level magnetic dipole moments of arbitrary physical states in the heterotic string theory. These results are then applied to study whether fundamental strings can consistently describe the microphysics of the black hole horizon in the case of a general classical solution characterized by mass, charge and angular momentum.     

Quasistationary collapse to the extreme Kerr black hole

It is shown that the extreme Kerr black hole, i.e. the one with the maximal angular momentum for a given mass, is the only candidate for a black hole limit of rotating fluid bodies in equilibrium.     

Horizon structure of rotating Bardeen black hole and particle acceleration

We investigate the horizon structure and ergosphere in a rotating Bardeen regular black hole, which has an additional parameter (g) due to the magnetic charge, apart from the mass (M) and the rotation parameter (a). Interestingly, for each value of the parameter g, there exists a critical rotation parameter (\(a=a_{E}\)), which corresponds to an extremal black hole with degenerate horizons, while for \(a<a_{E}\) it describes a non-extremal black hole with two horizons, and no black hole for \(a>a_{E}\). We find that the extremal value \(a_E\) is also influenced by the parameter g, and so is the ergosphere. While the value of \(a_E\) remarkably decreases when compared with the Kerr black hole, the ergosphere becomes thicker with the increase in g. We also study the collision of two equal mass particles near the horizon of this black hole, and explicitly show the effect of the parameter g. The center-of-mass energy (\(E_\mathrm{CM}\)) not only depend on the rotation parameter a, but also on the parameter g. It is demonstrated that the \(E_\mathrm{CM}\) could be arbitrarily high in the extremal cases when one of the colliding particles has a critical angular momentum, thereby suggesting that the rotating Bardeen regular black hole can act as a particle accelerator.     

Vaidya spacetime in the diagonal coordinates

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric and cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g ₀₀ = 0 or g ₀₀ = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.     

Motion and collision of particles near Plebanski-Demianski black hole: Shadow and gravitational lensing

Here we consider accelerating and rotating charged Plebanski-Demianski (PD) class of black hole metric as a particle accelerator. We obtain the geodesic motions (timelike, null and spacelike) of particles in a non-equatorial plane around the PD black hole. We find the effective potential, energy, angular momentum, impact parameters, and discuss the circular orbit. We study the center of mass energy of two neutral particles falling from infinity to near the non-extremal horizons (event and Cauchy horizons), extremal horizon, accelerating horizons, and near the center of the PD black hole. Also, we study the collision of a particle and a massless photon. Then we find the center of mass energy due to the collision of two massless photons in the PD black hole background. We compute the redshift and blueshift of the emitted photons by massive particles while light signal travels along null geodesics towards the observer located far away from the source. We study the Penrose process, which occurs within the ergosphere, and examines the particle’s motion with its implications. Here, we analyze the PD black hole shadow’s apparent shape, which forms far away from the black hole. We study the possible visibility of the PD black hole through photon’s shadow and energy emission rate. We also investigate the effect on the shadow of the PD black hole in plasma for a distant observer. We study the strong gravitational lensing by PD black hole. Finally, we analyze the deflection angle, lens equation, position, magnification, Einstein ring and observables by taking the supermassive PD black hole in the Galaxy’s center.     

Spin and mass of the nearest supermassive black hole

Quasi-periodic oscillations (QPOs) of the hot plasma spots or clumps orbiting an accreting black hole contain information on the black hole mass and spin. The promising observational signatures for the measurement of black hole mass and spin are the latitudinal oscillation frequency of the bright spots in the accretion flow and the frequency of black hole event horizon rotation. Both of these frequencies are independent of the accretion model and defined completely by the properties of the black hole gravitational field. Interpretation of the known QPO data by dint of a signal modulation from the hot spots in the accreting plasma reveals the Kerr metric rotation parameter, \(a=0.65\pm 0.05\) , and mass, \(M=(4.2\pm 0.2)10^6M_\odot \) , of the supermassive black hole in the Galactic center. At the same time, the observed 11.5 min QPO period is identified with a period of the black hole event horizon rotation, and, respectively, the 19 min period is identified with a latitudinal oscillation period of hot spots in the accretion flow. The described approach is applicable to black holes with a low accretion rate, when accreting plasma is transparent up to the event horizon region.     

A variational principle for black holes

It is shown that the initial data which gives rise to stationary black hole solutions extremizes the mass for a given angular momentum and area of the horizon. The only extremum of the mass for a given area of the horizon but arbitrary angular momentum is the Schwarzschild solution. In this case, and when the angular momentum is small, the extremum of the mass is a local minimum. This suggests that the initial data for the Schwarzschild solution has a smaller mass than any other initial data with the same area of the horizon. If this is the case, there is no possibility of proving the occurrence of naked singularities by methods suggested by Penrose and Gibbons. Together with Carter's theorem, the fact that the extremum is a local minimum indicates that the Kerr solutions are stable against axisymmetric perturbations.