A new model for QPOs in accreting black holes: application to the microquasar GRS 1915+105

In this paper we extend the idea suggested previously by Pétri (Astron. Astrophys. 439:L27, 2005a; 443:777, 2005b) (papers I and II) that the high frequency quasi-periodic oscillations (HF-QPOs) observed in low-mass X-ray binaries (LMXBs) may be explained as a resonant oscillation of the accretion disk with a rotating asymmetric background (gravitational or magnetic) field imposed by the compact object. Here, we apply this general idea to black hole binaries. It is assumed that a test particle experiences a similar parametric resonance mechanism such as the one described in paper I and II but now the resonance is induced by the interaction between a spiral density wave in the accretion disk, excited close to the innermost stable circular orbit, and vertical epicyclic oscillations. We use the Kerr spacetime geometry to deduce the characteristic frequencies of this test particle. The response of the test particle is maximal when the frequency ratio of the two strongest resonances is equal to 3:2 as observed in black hole candidates. Finally, applying our model to the microquasar GRS 1915+105, we reproduce the correct value of several HF-QPOs. Indeed the presence of the 168/113/56/42/28 Hz features in the power spectrum time analysis is predicted. Moreover, based only on the two HF-QPO frequencies, our model is able to constrain the mass M _BH and angular momentum a _BH of the accreting black hole. We show the relation between M _BH and a _BH for several black hole binaries. For instance, assuming a black hole weakly or mildly rotating, i.e. a _BH≤0.5?G? M _BH/c ², we find that for GRS 1915+105 its mass satisfies 13?M _⊙≤M _BH≤20?M _⊙. The same model applied to two other well-known BHCs gives for GRO J1655-40 a mass 5?M _⊙≤M _BH≤7?M _⊙ and for XTE J1550-564 a mass 8?M _⊙≤M _BH≤11?M _⊙. This is consistent with other independent estimations of the black hole mass. Finally for H1743-322, we found the following bounds, 9?M _⊙≤M _BH≤13?M _⊙.     

Strong gravitational lensing in a charged squashed Kaluza-Klein black hole

In this paper we investigate the strong gravitational lensing in a charged squashed Kaluza-Klein black hole. We suppose that the supermassive black hole in the galaxy center can be considered by a charged squashed Kaluza-Klein black hole and then we study the strong gravitational lensing theory and estimate the numerical values for parameters and observables of it. We explore the effects of the scale of extra dimension ρ ₀ and the charge of black hole ρ _q on these parameters and observables.     

The equal area law of asymptotically AdS black holes in extended phase space

According to Maxwell’s equal area law we study the “real” phase diagram of the charged AdS black hole and the Kerr-AdS black hole. In the extended phase space constructed by treating the cosmological constant as pressure, the two kinds of AdS black hole display themselves like van der Waals system. Under the critical temperature T _c , there exists a regime where the condition of stable equilibrium will be violated. We employ the equal area law to find an isobar which is the real two phase coexistence line. As a byproduct we find a simple method to derive the critical value of the thermodynamic quantities.     

Schwarzschild black hole in dark energy background

In this paper we present an exact solution of Einstein’s field equations describing the Schwarzschild black hole in dark energy background. It is also regarded as an embedded solution that the Schwarzschild black hole is embedded into the dark energy space producing Schwarzschild-dark energy black hole. It is found that the space-time geometry of Schwarzschild-dark energy solution is non-vacuum Petrov type D in the classification of space-times. We study the energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor of the Schwarzschild-dark energy solution. We also find that the energy-momentum tensor of the Schwarzschild-dark energy solution violates the strong energy condition due to the negative pressure leading to a repulsive gravitational force of the matter field in the space-time. It is shown that the time-like vector field for an observer in the Schwarzschild-dark energy space is expanding, accelerating, shearing and non-rotating. We investigate the surface gravity and the area of the horizons for the Schwarzschild-dark energy black hole.     

Vaidya black hole in non-stationary de Sitter space: Hawking’s temperature

In this paper we present a class of non-stationary solutions of Einstein’s field equations describing embedded Vaidya-de Sitter black holes with a cosmological variable function Λ(u). The Vaidya-de Sitter black hole is interpreted as the radiating Vaidya black hole is embedded into the non-stationary de Sitter space with variable Λ(u). The energy-momentum tensor of the Vaidya-de Sitter black hole is expressed as the sum of the energy-momentum tensors of the Vaidya null fluid and that of the non-stationary de Sitter field, and satisfies the energy conservation law. We study the energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor. We find the violation of the strong energy condition due to the negative pressure and leading to a repulsive gravitational force of the matter field associated with Λ(u) in the space-time. We also find that the time-like vector field for an observer in the Vaidya-de Sitter space is expanding, accelerating, shearing and non-rotating. It is also found that the space-time geometry of non-stationary Vaidya-de Sitter solution with variable Λ(u) is Petrov type D in the classification of space-times. We also find the Vaidya-de Sitter black hole radiating with a thermal temperature proportional to the surface gravity and entropy also proportional to the area of the cosmological black hole horizon.     

Formation of black holes through BSW effect and black hole–black hole collisions

We study mechanism of formation of black holes (BHs) from collisions of particles in the vicinity of the supermassive black hole acting as a particle accelerator trough BSW (Banados-Silk-West) effect. Moreover, we also investigate BH-BH collision, in which stellar black holes colliding near the horizon of a rotating supermassive black hole can reach large values of the center-of-mass energy. This result implies that high arbitrary energy of collisions causes to be transformed into radiation energy and particles, which might bring possible visible signals through the astrophysical observations. We study the radiation energy from a collision of two accelerating stellar black holes and find a maximal value of the radiation energy to be nearly E _rad ≈2.5?10⁵⁶ erg for the ultrarelativistic value of v/c=0.99 from BH-BH collisions.     

The Newtonian forces in the Kerr geometry

We study the properties of the ’Newtonian forces’ acting on a test particle in the field of the Kerr black hole geometry. We show that the centrifugal force and the Coriolis force reverse signs at several different locations. We point out the possible relevance of such reversals particularly in the study of the stability properties of the compact rotating stars and the accretion discs in hydrostatic equilibria Received honourable mention in the 1989 Gravity Research Foundation essay competition.     

Entropic gravity resulting from a Yukawa type of correction to the metric for a solar mass black hole

There has been a renewed interest in the recent years in the possibility of deviations from the predictions of Newton’s “inverse-square law” of universal gravitation. One of the reasons for renewing this interest lies in various theoretical attempts to construct a unified elementary particle theory, in which there is a natural prediction of new forces over macroscopic distances. In this paper we study the entropic gravity correction to the gravitational force on the horizon of a black hole whose metric has been modified by a Yukawa term. We find that the gravitational radius of such a black hole is given in-terms of the Lambert function, and the entropic force introduces a extra term that depends on the square of the coupling constant α of the Yukawa potential. In the case alpha equals zero we recover the Newtonian gravitational force on the horizon. In a first effort to obtain a relation between geometry and information, we calculate the Ricci scalar and through entropy we establish a relation to the number of information N where this is given in nats. Finally, we calculate a critical entropy value as well as a critical information number N _c for which the curvature becomes identically zero which implies that the space becomes flat.     

Orbital dynamics of the gravitational field in Bardeen space-time

In this paper, the orbital dynamics of the gravitational field in Bardeen space-time are investigated. The equations of the particle’s orbital motion are given by solving the Lagrangian equation, and the stability and types of orbits are studied by means of analysing the effective potential of particles. Also, with the help of phase-plane method, the closed and non-closed orbits of test particle are analysed. We find that the stability and types of orbits in the Bardeen space-time are determined not only by the particles’ energy but also by the angular momentum. And for q=0.5M and b<3.3731M, absorbed by the black hole is the only fate of the test particle. We also find that the position of the innermost stable circular orbit of Bardeen black hole occurs at r _min =5.5722M.     

Shadow of rotating Hořava-Lifshitz black hole

The shadow of rotating Ho?ava-Lifshitz black hole has been studied and it was shown that in addition to the specific angular momentum a, parameters of Ho?ava-Lifshitz spacetime essentially deform the shape of the black hole shadow. For a given value of the black hole spin parameter a, the presence of a parameter Λ _W and KS parameter ω enlarges the shadow and reduces its deformation with respect to the one in the Kerr spacetime. We have found a dependence of radius of the shadow R _s and distortion parameter δ _s from parameter Λ _W and KS parameter ω both. Optical features of the rotating Ho?ava-Lifshitz black hole solutions are treated as emphasizing the rotation of the polarization vector along null congruences. A comparison of the obtained theoretical results on polarization angle with the observational data on Faraday rotation measurements provides the upper limit for the δ parameter as δ≤2.1?10^?3.     

Structure and stability of rotating fluid disks around massive objects. II. General relativistic formulation

In this paper we have considered the structure of a thick perfect fluid disk of constant density rotating around a Schwarzschild black hole and its stability under axisymmetric perturbation. The inner edge of such disk cannot lie within 4m. The critical γ_c for neutral stability is found to be much less than 4/3 indicating that the disks are generally stable     

Isofrequency pairing of circular orbits in Schwarzschild spacetime in the presence of magnetic field

We study isofrequency pairing of the circular non-geodesic orbits in the vicinity of the Schwarzschild black hole immersed in external asymptotically uniform magnetic field. The dependence of the isofrequency pairing of non-geodesic orbits from the special quantities, such as radius of the innermost stable circular orbits (ISCO), radius of the circular orbits (r _b ) at the limit e(eccentricity)→0, and from the value of the small quantity ξ=(r _b ?r _ISCO) of the particles moving around the Schwarzschild black hole in the presence of the magnetic field has been found. It is shown that presence of the magnetic field gives rise to the r _ISCO and r _b of the particles to be slightly shifted from black hole and the contribution of the quantity ξ decreases the amount of isofrequency pairing of non-geodesic orbits due to the reduction of the surface of the region between the separatrix and circular-orbit duals (COD). We study the dependence of surface of region where particles can move and isofrequency pairing of non-geodesic orbits occur around the Schwarzschild black hole from the magnetic field. We find a decrease of nearly (7–10) % for the maximal values of the magnetic field B～10⁶–10⁷ Gauss in the surface of region where isofrequency pairing occurs around central object with compare to the one around Schwarzschild black hole without magnetic field. This result implies that it makes easier to identify signals through the astrophysical observations of compact objects in the presence of magnetic field.     

Hawking radiation of scalars from accelerating and rotating black holes with NUT parameter

We study the quantum tunneling of scalars from charged accelerating and rotating black hole with NUT parameter. For this purpose we use the charged Klein-Gordon equation. We apply WKB approximation and the Hamilton-Jacobi method to solve charged Klein-Gordon equation. We find the tunneling probability of outgoing charged scalars from the event horizon of this black hole, and hence the Hawking temperature for this black hole     

Massive antigravity field and incomplete black hole evaporation

If gravity is a mixture of the ordinary attractive force carried by the massless graviton, and of a repulsive force carried by a particle with nonzero mass, an evaporating black hole might leave a stable remnant.     

On the observability of the magnetic precession of the black hole accretion disks

The precession of a rotating charged black hole in an external magnetic field is considered. The possibility of observing the effect in black hole systems with magnetized accretion, disks is discussed.     

Relativistic Rotational Darkening of Lightlike Radiation and Von Zeipel's Theorem for Radially Emitting Spheroids

It is shown that an outgoing null radiation field in the outer space of a Kerr-Newman black hole is darkened by the rotation of the black hole. This rotational darkening is calculated for a spheroid emitting null radiation normally to its surface, yielding the von Zeipel-like effectthat the equatorial region is darkened more strongly than the polar regions.This effect is not confined to the case of black holes but is also observable for relativistically rotating fluid spheroids such as atmospheres of pulsars or neutron stars. Moreover, application to Hawking radiation suggests that the black hole cannot be viewed as a classical black body but that the Hawking radiationis a global geometric effect. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electromagnetic fields and charged particle motion around magnetized wormholes

We perform a study to describe motion of charged particles under the influence of electromagnetic and gravitational fields of a slowly rotating wormhole with nonvanishing magnetic moment. We present analytic expression for potentials of electromagnetic field for an axially symmetric slowly rotating magnetized wormholes. While addressing important issues regarding the subject, we compare our results of motion around black holes and wormholes in terms of the ratio of radii of event horizons of a black hole and of the throat of a wormhole. It is shown that both radial and circular motions of test bodies in the vicinity of a magnetized wormhole could give rise to a peculiar observational astrophysical phenomenon.     

A comparison of the entropies of collapsing stars and black holes

We considered three modes of black hole formation: (I) a black hole kernel first forms at the centre of a collapsing star and as the outer matter falls, the kernel grows until the whole star becomes a black hole; (II) all the layers of a collapsing simultaneously satisfy the Schwarzschild condition; (III) the outermost layer first satisfies the Schwarzschild condition. For each mode, we calculated the entropy carried by the collapsing matter, S_m, and the entropy of the black hole so formed, S_BH. We found S_BH to be 10¹⁹ times S_m and the lower limit of the mass capable of becoming a black hole to be the Planck mass, M_p = 10^?5g. A discussion on the nature of S_BH led us to think that S_BH possibly contains things other than the ordinary thermodynamical entropy.     

Energetics of magnetized black holes: Effective ergospheres and superradiance

The model of a black hole rotating in an external magnetic field is considered. The mechanisms of the energy extraction from the black hole in terms of the effective ergospheres for charged particles are described. It is shown that the external magnetic field essentially influences the boundaries of the effective ergospheres and the superradiance threshold.     

Energetics of the Kerr-Newman black hole by the penrose process

We have studied in detail the energetics of Kerr-Newman black hole by the Penrose process using charged particles. It turns out that the presence of electromagnetic field offers very favourable conditions for energy extraction by allowing for a region with enlarged negative energy states much beyondr = 2M, and higher negative values for energy. However, when uncharged particles are involved, the efficiency of the process (defined as the gain in energy/input energy) gets reduced by the presence of charge on the black hole in comparison with the maximum efficiency limit of 20.7 per cent for the Kerr black hole. This fact is overwhelmingly compensated when charged particles are involved as there exists virtually no upper bound on the efficiency. A specific example of over 100 per cent efficiency is given.