The model is constructed to describe the Schwarzschild-like black hole enclosed in the dust cosmological background. It is an exact solution of Einstein equations for spherically symmetric dust distribution, and is a special case of Lemaitre-Tolman-Bondi solutions. The motion of the test particle in the model is investigated in comoving coordinate frame. Observable velocity of the particle is found from geodesic equations. It is shown that chosen reference system does not allow to solve the problem of 'all or nothing' behavior.
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We construct regular rotating black hole and no-horizon spacetimes based on the recently introduced spherically symmetric generic regular black hole spacetimes related to electric or magnetic charge under nonlinear electrodynamics coupled to general relativity that for special values of the spacetime parameters reduce to the Bardeen and Hayward spacetimes. We show that the weak and strong energy conditions are violated inside the Cauchy horizons of these generic rotating black holes. We give the boundary between the rotating black hole and no-horizon spacetimes and determine the black hole horizons and the boundary of the ergosphere. We introduce the separated Carter equations for the geodesic motion in these rotating spacetimes. For the most interesting new class of the regular spacetimes, corresponding for magnetic charges to the Maxwell field in the weak field limit of the nonlinear electrodynamics, we determine the structure of the circular geodesics and discuss their properties. We study the epicyclic motion of a neutral particle moving along the stable circular orbits around the "Maxwellian" rotating regular black holes. We show that epicyclic frequencies measured by the distant observers and related to the oscillatory motion of the neutral test particle along the stable circular orbits around the rotating singular and regular Maxwellian black holes are always smaller than ones in the Kerr spacetime.
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We investigate ringed accretion disks composed of two tori (rings) orbiting on the equatorial plane of a central supermassive Kerr black hole. We discuss the emergence of the instability phases of each ring of the macro-configuration (ringed disk) according to the Paczynski violation of mechanical equilibrium. In the full general relativistic treatment, we consider the effects of the geometry of the Kerr spacetimes relevant to the characterization of the evolution of these configurations. The discussion of ring stability in different spacetimes enables us to identify particular classes of central Kerr attractors depending on their dimensionless spin. As a result of this analysis, we set constraints on the evolutionary schemes of the ringed disks relative to the torus morphology and on their rotation relative to the central black hole and to each other. The dynamics of the unstable phases of this system is significant for the high-energy phenomena related to accretion onto supermassive black holes in active galactic nuclei and the extremely energetic phenomena in quasars, which could be observed in their X-ray emission.
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We demonstrate that in the framework of standard general relativity, polytropic spheres with properly fixed polytropic index n and relativistic parameter σ , giving a ratio of the central pressure pc to the central energy density ρc , can contain a region of trapped null geodesics. Such trapping polytropes can exist for n >2.138 , and they are generally much more extended and massive than the observed neutron stars. We show that in the n - σ parameter space, the region of allowed trapping increases with the polytropic index for intervals of physical interest, 2.138 0.677 from the allowed region. In order to relate the trapping phenomenon to astrophysically relevant situations, we restrict the validity of the polytropic configurations to their extension rextr corresponding to the gravitational mass M ∼2 M⊙ of the most massive observed neutron stars. Then, for the central density ρc∼1 015 g cm-3 , the trapped regions are outside rextr for all values of 2.138 c∼5 ×1 015 g cm-3 , the whole trapped regions are located inside rextr for 2.138 c∼1 016 g cm-3 , the whole trapped regions are inside rextr for all values of 2.138 Read More
Quintessential dark energy with density ρ and pressure p is governed by an equation of state of the form p=ωqρ with the quintessential parameter ω_qin (-1;-1/3). We derive the geometry of quintessential rotating black holes, generalizing thus the Kerr spacetimes. Then we study the quintessential rotating black hole spacetimes with the special value of ωq = -2/3 when the resulting formulae are simple and easily tractable. We show that such special spacetimes can exist for the dimensionless quintessential parameter c < 1/6 and determine the critical rotational parameter a0 separating the black hole and naked singularity spacetime in dependence on the quintessential parameter c . For the spacetimes with ωq = -2/3 we give all the black hole characteristics and demonstrate local thermodynamical stability. We present the integrated geodesic equations in separated form and study in details the circular geodetical orbits. We give radii and parameters of the photon circular orbits, marginally bound and marginally stable orbits. We stress that the outer boundary on the existence of circular geodesics, given by the so-called static radius where the gravitational attraction of the black hole is balanced by the cosmic repulsion, does not depend on the dimensionless spin of the rotating black hole, similarly to the case of the Kerr-de Sitter spacetimes with vacuum dark energy. We also give restrictions on the dimensionless parameters c and a of the spacetimes allowing for existence of stable circular geodesics. Finally, using numerical methods we generalize the discussion of the circular geodesics to the black holes with arbitrary quintessential parameter ωq.
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We study the shadow of the rotating black hole with quintessential energy (i) in vacuum, (ii) in the presence of plasma with radial power-law density. For the vacuum case, the quintessential field parameter of the rotating black hole significantly changes the shape of the shadow. With increasing quintessential field parameter, the radius of the shadow also increases. With the increase of the radius of the shadow of the rotating black hole, the quintessential field parameter causes decrease of the distortion of the shadow shape: in the presence of the quintessential field parameter, the shadow of the fast rotating black hole becomes too close to the circle. We assume the distant observer of the black hole shadow to be located near the so-called static radius where the gravitational attraction of the black hole is just balanced by the cosmic repulsion. The shape and size of the shadow of quintessential rotating black hole surrounded by plasma depends on (i) plasma parameters, (ii) black hole spin and (iii) quintessential field parameter. With the increase of the plasma refraction index, the apparent radius of the shadow increases. However, for the large values of the quintessential field parameter, the change of the black hole shadow shape due to the presence of plasma is not significant, i.e. the effect of the quintessential field parameter dominates over the plasma effect.
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A new intrinsically-relativistic kinetic mechanism for generation of nonisotropic relativistic kinetic equilibria in collisionless N-body systems is pointed out. The theory is developed in the framework of the covariant Vlasov statistical description. The new effect is based on the constraints placed by the conservation laws of neutral single-particle dynamics in prescribed background curved-spacetimes demonstrating existence of Killing tensors. As an illustration, the particular case of the Kerr spacetime admitting the so-called Carter constant for the particle geodesic motion is considered. The general functional form of the equilibrium kinetic distribution function (KDF) is determined and an explicit realization in terms of Gaussian-like distributions is provided. It is shown that, due to the Carter constant, these equilibrium KDFs exhibit an anisotropic phase-space functional dependence in terms of the single-particle 4-velocity components, giving rise to corresponding nonisotropic continuum fluid fields. The qualitative properties of the equilibrium stress-energy tensor associated with these systems are discussed, with a particular emphasis on the related occurrence of temperature anisotropy effects. The theory is susceptible of astrophysical applications, including in particular the statistical properties of dark matter (DM) halos around stellar-mass or galactic-center black holes.
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In the weak field approximation, we study the gravitational lensing near the regular Bardeen, Hayward and Ayon-Beato-Garcia (ABG) black holes surrounded by plasma. The exact expressions for the deflection angle of the photons due to the effect of the gravitational field and the plasma have been obtained. The analysis of the image source brightness magnification in the background spacetimes of (i) Bardeen, (ii) Hayward and (iii) ABG regular black holes have shown that the increase of the corresponding charge of regular black hole causes the increase in the magnification of the source image. In addition to the primary ring, one may observe the secondary ring with smaller magnification. The influence of the plasma with (i) constant and (ii) radial power law electron density to the magnification of the source image has been studied.
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Twin-peak quasi-periodic oscillations (QPOs) are observed in the X-ray power-density spectra of several accreting low-mass neutron star (NS) binaries. In our previous work we have considered several QPO models. We have identified and explored mass-angular-momentum relations implied by individual QPO models for the atoll source 4U 1636-53. In this paper we extend our study and confront QPO models with various NS equations of state (EoS). We start with simplified calculations assuming Kerr background geometry and then present results of detailed calculations considering the influence of NS quadrupole moment (related to rotationally induced NS oblateness) assuming Hartle-Thorne spacetimes. We show that the application of concrete EoS together with a particular QPO model yields a specific mass-angular-momentum relation. However, we demonstrate that the degeneracy in mass and angular momentum can be removed when the NS spin frequency inferred from the X-ray burst observations is considered. We inspect a large set of EoS and discuss their compatibility with the considered QPO models. We conclude that when the NS spin frequency in 4U 1636-53 is close to 580 Hz, we can exclude 51 of the 90 considered combinations of EoS and QPO models. We also discuss additional restrictions that may exclude even more combinations. Namely, 13 EOS are compatible with the observed twin-peak QPOs and the relativistic precession model. However, when considering the low-frequency QPOs and Lense-Thirring precession, only 5 EOS are compatible with the model.
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In this work we have obtained the set of new exact solutions of Einstein
equations that generalize the known LTB solution for the particular case
of nonzero pressure under zero spatial curvature. These solutions are
pretending to describe the black hole immersed in nonstatic cosmological
background and give a possibility to investigate the hot problems
concerning the effects of the cosmological expansion in gravitationally
bounded systems and other related problems. It was shown that each of
the solutions obtained contains either the Reissner-Nordstrom or the
Schwarzschild black hole in the central region of the space. It is
demonstrated that the approach of the mass function use in solving the
Einstein equations allows clear physical interpretation of the resulting
solutions that is of much benefit to any their concrete application.
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