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.
This paper is devoted to investigate the cold plasma wave properties outside the event horizon of the Schwarzschild planar analogue. The dispersion relations are obtained from the corresponding Fourier analyzed equations for non-rotating and rotating, non-magnetized and magnetized backgrounds. These dispersion relations provide complex wave numbers. The wave numbers are shown in graphs to discuss the nature and behavior of waves and the properties of plasma lying in the vicinity of the Schwarzschild event horizon.
In this paper a solution for a static spherically symmetric body is thoroughly considered in the framework of the Relativistic Theory of Gravitation. By the comparison of this solution with the Schwarzschild solution in General Relativity their substantial difference is established in the region close to the Schwarzschild sphere. Just this difference excludes the possibility of collapse to form ``black holes''.
Point charge, radially moving in the vicinity of a black hole is considered. Electromagnetic field in wave zone and in the small neighbourhood of the charge is calculated. Numerical results of the calculation of the spectrum of electromagnetic radiation of the point charge are presented. Covariant approach for the calculation of electromagnetic self-force is used for the case of the slowly moving charge. Numerical results for the self-force in the case of slow motion of the particle are obtained and compared to the results in literature.
Two particle collisions close to the horizon of the rotating nonextremal Kerr's and Schwarzschild black holes are analyzed. For the case of multiple collisions it is shown that high energy in the centre of mass frame occurs due to a great relative velocity of two particles and a large Lorentz factor. The dependence of the relative velocity on the distance to horizon is analyzed, the time of movement from the point in the accretion disc to the point of scattering with large energy as well as the time of back movement to the Earth are calculated. It is shown that they have reasonable order.
We investigate the time evolution of the redshift of the spectrum of electromagnetic radiation that is emitted by the star that moves in the vicinity of supermassive black hole. For the case of Schwarzschild black hole we solve this problem exactly in General Theory of Relativity. Also we formulate an approach that gives possibilities to solve the inverse problem: reconstruction of motion of a star in the vicinity of black hole using the redshift data. This approach consists of two steps. The first step gives possibilities to find unique solution for the integrals of motion of the star by solu…
The claim that the microstates of Schwarzschild black holes in perturbative string theory amount to the modes of long folded strings in the vicinity of its horizon is supported by more evidence.
The equations governing general relativistic, spherically symmetric, hydrodynamic accretion of polytropic fluid onto black holes are solved in Schwarzschild metric to investigate some of the transonic properties of the flow. Only stationary solutions are discussed. For such accretion, it has been shown that real physical sonic points may form {\it even for flow with $γ< {4/3}$ or $γ> {5/3}$}. Behaviour of some flow variables in the close vicinity of the event horizon are studied as a function of specific energy and polytropic index of the flow.
Usually alternative theories of gravity imply deviations from the well-known Kerr space-time, a model of an isolated black hole in General Relativity. In the dominant order, the deformed Kerr metric, free of closed time-like curves outside the event horizon, has been suggested recently by Johannsen and Psaltis. It has a single deformation parameter which is not constrained by the current observations, allowing, thereby, for a kind of unified and simple phenomenological description of black holes in various theories of gravity. Here we consider a number of classical and quantum phenomena of rad…
We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential, and a toy model for the time-dependent evolution of the potential when immersed in a slowly cooling radiation bath. Through these numerical investigations, we aim to improve our understanding of the non-equilibrium dynamics of a symmetry breaking field (such as the Higgs) in the vicinity of a compact object such as a black hole. Understanding this dynamics may suggest new approaches for stu…
In this work we study the effects of non-minimal coupling between electromagnetism and gravity, which are motivated by quantum effects such as vacuum polarization. We investigate the modification of both asymptotically dipole and uniform magnetic fields around a Schwarzschild black hole that come as the result of non-minimal coupling. While in both cases the magnetic field gets enhanced or suppressed with respect to the case of minimal coupling, depending on the sign of non-minimal coupling parameter, in the case of a background uniform magnetic field the direction of the magnetic field also a…
The Cosmic Blackbody Background Radiation pervades the entire Universe, and so falls into every astrophysical black hole. The blueshift of the infalling photons, measured by a static observer, is infinite at the event horizon. This raises a question as to whether a "firewall" of high energy density may form just outside the horizon, or whether the effect can be attributed exclusively to a singular behavior of the static observer's frame at the horizon. In principle, the presence of such firewall may alter the motion of the infalling matter, influence the black hole evolution, or even invalidat…
We investigate the dynamics of a neutral and a charged particle around a static and spherically symmetric black hole in the presence of quintessence matter and external magnetic field. We explore the conditions under which the particle moving around the black hole could escape to infinity after colliding with another particle. The innermost stable circular orbit (ISCO) for the particles are studied in detail. Mainly the dependence of ISCO on dark energy and on the presence of external magnetic field in the vicinity of black hole is discussed. By using the Lyapunov exponent, we compare the stab…
We illustrate how Hawking's radiance from a Schwarzschild black hole is modified by the electrostatic self-interaction of the emitted charged particles. A W.K.B approximation shows that the probability for a self-interacting charged particle to propagate from the interior to the exterior of the horizon is increased relative to the corresponding probability for neutral particles. We also demonstrate how the electric potential of a charged test object in the black hole's vicinity gives rise to pair creation. We analyze this phenomenon semiclassically by considering the existence of the appropria…
We study the Page curve for asymptotically flat eternal Schwarzschild black holes in four and higher spacetime dimensions. Before the Page time, the entanglement entropy grows linearly in time. After the Page time, the entanglement entropy of a given region outside the black hole is largely modified by the emergence of an island, which extends to the outer vicinity of the event horizon. As a result, it remains a constant value which reproduces the Bekenstein-Hawking entropy, consistent with the finiteness of the von Neumann entropy for an eternal black hole.
We developed realistic fully general relativistic computer code for simulation of optical projection in a strong, spherically symmetric gravitational field. Standard theoretical analysis of optical projection for an observer in the vicinity of a Schwarzschild black hole is extended to black hole spacetimes with a repulsive cosmological constant, i.e, Schwarzschild-de Sitter spacetimes. Influence of the cosmological constant is investigated for static observers and observers radially free-falling from static radius. Simulation includes effects of gravitational lensing, multiple images, Doppler …
The interaction of a charged particle with its own field results in the "self-force" on the particle, which includes but is more general than the radiation reaction force. In the vicinity of the particle in curved spacetime, one may follow Dirac and split the retarded field of the particle into two parts, (1) the singular source field, ~q/r, and (2) the regular remainder field. The singular source field exerts no force on the particle, and the self-force is entirely caused by the regular remainder. We describe an elementary multipole decomposition of the singular source field which allows for …
The interaction of a charged particle with its own field results in the "self-force" on the particle, which includes but is more general than the radiation reaction force. In the vicinity of the particle in curved spacetime, one may follow Dirac and split the retarded field of the particle into two parts, (1) the singular source field, \sim q/r, and (2) the regular remainder field. The singular source field exerts no force on the particle, and the self-force is entirely caused by the regular remainder. We describe an elementary multipole decomposition of the singular source field which allows …
The motion of a massive test particle in a Schwarzschild spacetime surrounded by a perfect fluid with equation of state $p_0= w ρ_0$ is investigated. Deviations from geodesic motion are analyzed as a function of the parameter $w$, ranging from $w=1$ which corresponds to the case of massive free scalar fields, down into the so-called "phantom" energy, with $w<-1$. It is found that the interaction with the fluid distribution leads to capture (escape) of the particle trajectory in the case $1+w>0$ ($<0$), respectively. Based on this result, it is argued that inspection of the trajectories of test…
In this paper, geodesic motion of the charged particles in the vicinity of event horizon of Schwarzschild anti-de-Sitter black hole (BH) with topological defects has been investigated. Weakly magnetized environment is considered in the surrounding of BH which only effects the motion of the particles and doesn't effect the geometry of the BH. Hence, particles are under the influence of gravity and electromagnetic forces. We have explored the effect of magnetic field on the trajectories of the particles and more importantly on the position of the innermost stable circular orbit. It is observed t…
A gravitational theory is formulated by considering the physical processes underlying relativistic dilation of time and contraction of space. It is shown that the point mass solution of general relativity's field equation - the Schwarzschild metric - is a weak-field approximation to the more general Lagrangian resulting here. Unlike general relativity the resulting theory does not exhibit a singularity at the Schwarzschild radius and furthermore shows that photons escape from that radius with a red shift of e^0.5 - 1. Consequently black holes are not black. Experimental confirmations of genera…
Classical (quasinormal) and quantum (Hawking) radiations are investigated for test fields in the background of a four dimensional, spherically symmetric and asymptotically flat black hole in the Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The geometry of the EdGB black hole deviates from the Schwarzschild geometry only slightly. Therefore, here we observe that the quasinormal spectrum also deviates from its Schwarzschild limit at most moderately, allowing for a $9\%$ decrease in the damping rate and up to a $6\%$ decrease in the real oscillation frequency. However, the intensity of Hawking ra…
The order $\hbar$ fluctuations of gauge fields in the vicinity of a blackhole can create a repulsive antigravity region extending out beyond the renormalized Schwarzschild horizon. If the strength of this repulsive force increases as higher orders in the back-reaction are included, the formation of a wormhole-like object could occur.
We present here a detailed study of the quasi-normal spectrum of brane-localised Standard Model fields in the vicinity of D-dimensional black-holes. A variety of such backgrounds (Schwarzschild, Reissner-Nordstrom and Schwarzszchild-(Anti) de Sitter) are investigated. The dependence of the quasi-normal spectra on the dimensionality D, spin of the field s, and multipole number l is analyzed. Analytical formulae are obtained for a number of limiting cases: in the limit of large multipole number for Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordstrom black holes, in the extremal limit o…
We investigate particle motion in the vicinity of a $4D$ Einstein-Gauss-Bonnet (EGB) black hole immersed in external asymptotically uniform magnetic field. It is well known that magnetic fields can strongly affect charged particle motion in the black hole vicinity due to the Lorenz force. We find that the presence of the Gauss-Bonnet (GB) coupling gives rise to a similar effect, reducing the radius of the innermost stable circular orbit (ISCO) with respect to the purely relativistic Schwarzschild black hole. Further, we consider particle collisions in the black hole vicinity to determine the c…
Chaotic motion and power spectral density in Schwarzschild Bertotti-Robinson black hole spacetime
Harbin Institute of Technology（哈尔滨工业大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；Institute of Fundamental and Applied Research, National Research University TIIAME（TIIAME国立研究型大学基础与应用研究所）；Tashkent State Technical University（塔什干国立技术大学）
In this letter we calculate the gravitational waves (GWs) emitted from a small binary (SB) by solving the Teukolsky equation in the background of a massive exotic compact object (ECO) which is phenomenologically described by a Schwarzschild geometry with a reflective boundary condition at its "would-be" horizon. The "continuous echo" waves propagating to infinity due to reflectivity of ECO at its "would-be" horizon provide an exquisite probe to the nature of the ECO's horizon.
We study static quantum corrections of the Schwarzschild metric in the Boulware vacuum state. Due to the absence of a complete analytic expression for the full semiclassical Einstein equations we approach the problem by considering the s-wave approximation and solve numerically the associated backreaction equations. The solution, including quantum effects due to pure vacuum polarization, is similar to the classical Schwarzschild solution up to the vicinity of the classical horizon. However, the radial function has a minimum at a time-like surface close to the location of the classical event ho…
We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standar…
We investigate the general relativistic magnetohydrodynamic (GRMHD) equations for cold plasma around the Reissner-Nordström black hole. Applying 3+1 spacetime split we linearize the perturbed equations for non-magnetized/magnetized plasma in both rotating and non-rotating background. By Fourier analyze we then derive dispersion relations and investigate the existence of waves with positive angular frequency in the vicinity of the black hole horizon. The analysis finds propagation of negative phase and group velocities for rotating magnetized surroundings.
In order to test the role of large-scale magnetic fields in quasiperiodic oscillation phenomena observed in microquasars, we study oscillatory motion of charged particles in vicinity of a Schwarzschild black hole immersed into an external asymptotically uniform magnetic field. We determine the fundamental frequencies of small harmonic oscillations of charged test particles around stable circular orbits in the equatorial plane of a magnetized black hole, and discuss the radial profiles of frequencies of the radial and latitudinal harmonic oscillations in dependence on the mass of the black hole…
The higher derivative gravity includes corrections of the second order in curvature and allows for both Schwarzschild and non-Schwarzschild asymptotically flat black-hole solutions. Here we find the grey-body factors and energy emission rates for Hawking radiation of test Dirac and electromagnetic fields in the vicinity of such a non-Schwarzschild black hole. The temperature and mass of the black hole monotonically decrease from its Schwarzschild value to zero when the coupling constant is increased up to its extremal value. Nevertheless, for small and moderate values of the coupling constant …
We study motion of a charged particle in the vicinity of a weakly magnetized Schwarzschild black hole and focus on its bounded trajectories lying in the black hole equatorial plane. If the Lorentz force, acting on the particle, is directed outward from the black hole, there exist two qualitatively different types of trajectories, one is a curly motion and another one is a trajectory without curls. We calculated the critical value of the magnetic field for the transition between these two types. If the magnetic field is greater than the critical one, for fixed values of the particle energy and …
We investigate the possibility of spontaneous scalarization of static, spherically symmetric, and asymptotically flat black holes (BHs) in the Horndeski theory. Spontaneous scalarization of BHs is a phenomenon that the scalar field spontaneously obtains a nontrivial profile in the vicinity of the event horizon via the nonminimal couplings and eventually the BH possesses a scalar charge. In the theory in which spontaneous scalarization takes place, the Schwarzschild solution with a trivial profile of the scalar field exhibits a tachyonic instability in the vicinity of the event horizon, and evo…
We study strong gravitational lensing due to a Schwarzschild black hole. Apart from the primary and the secondary images we find a sequence of images on both sides of the optic axis; we call them {\em relativistic images}. These images are formed due to large bending of light near r = 3M (the closest distance of approach r_o is greater than 3M). The sources of the entire universe are mapped in the vicinity of the black hole by these images. For the case of the Galactic supermassive ``black hole'' they are formed at about 17 microarcseconds from the optic axis. The relativistic images are not r…
Regularity of the horizon radius $r_g$ of a collapsing body constrains a limiting form of a spherically-symmetric energy-momentum tensor near it. Its non-zero limit belongs to one of four classes that are distinguished only by two signs. As a result, close to $r_g$ the geometry can always be described by either an ingoing or outgoing Vaidya metric with increasing or decreasing mass. If according to a distant outside observer the trapped regions form in finite time, then the Einstein equations imply violation of the null energy condition. In this case the horizon radius and its rate of change d…
The construction of the conformal scalar propagator which has been obtained in the preceding two projects as an analytic function of the Schwarzschild black-hole space-time is completed with a boundary condition imposed by the physical context through contour integration in the exterior vicinity of the event horizon. It is shown that, as a consequence of the semi-classical character which the emitted quanta have in that exterior vicinity, the particle production by the Schwarzschild black hole which was formally established in the preceding project is identical to thermal Hawking radiation. By…
We investigate generation of electromagnetic radiation by gravitational waves interacting with a strong magnetic field in the vicinity of a vibrating Schwarzschild black hole. Such an effect may play an important role in gamma-ray bursts and supernovae, their afterglows in particular. It may also provide an electromagnetic counterpart to gravity waves in many situations of interest, enabling easier extraction and verification of gravity wave waveforms from gravity wave detection. We set up the Einstein-Maxwell equations for the case of odd parity gravity waves impinging on a static magnetic fi…
We consider the Burgers equation posed on the outer communication region of a Schwarzschild black hole spacetime. Assuming spherical symmetry for the fluid flow under consideration, we study the propagation and interaction of shock waves under the effect of random forcing. First of all, considering the initial and boundary value problem with boundary data prescribed in the vicinity of the horizon, we establish a generalization of the Hopf--Lax--Oleinik formula, which takes the curved geometry into account and allows us to establish the existence of bounded variation solutions. To this end, we …
We investigate the generation of electromagnetic and gravitational radiation in the vicinity of a perturbed Schwarzschild black hole. The gravitational perturbations and the electromagnetic field are studied by solving the Teukolsky master equation with sources, which we take to be locally charged, radially infalling, matter. Our results show that, in addition to the gravitational wave generated as the matter falls into the black hole, there is also a burst of electromagnetic radiation. This electromagnetic field has a characteristic set of quasinormal frequencies, and the gravitational radiat…
We study two different ways to analyze the Hawking evaporation of a Schwarzschild-de Sitter black hole. The first one uses the standard approach of surface gravity evaluated at the possible horizons. The second method derives its results via the Generalized Uncertainty Principle (GUP) which offers a yet different method to look at the problem. In the case of a Schwarzschild black hole it is known that this methods affirms the existence of a black hole remnant (minimal mass $M_{\rm min}$) of the order of Planck mass $m_{\rm pl}$ and a corresponding maximal temperature $T_{\rm max}$ also of the …
We have studied the wave properties of the cold and isothermal plasma in the vicinity of the Schwarzschild black hole event horizon. The Fourier analyzed perturbed 3+1 GRMHD equations are taken on the basis of which the complex dispersion relations are obtained for non-rotating, rotating non-magnetized and rotating magnetized backgrounds. The propagation and attenuation vectors along with the refractive index are obtained (shown in graphs) to study the dispersive properties of the medium near the event horizon. The results show that no information can be obtained from the Schwarzschild magneto…
Full set of scenarios of high energy collision in the Schwarzschild background and kinematic censorship
Centre for Cosmology and Science Popularization (CCSP)（宇宙学与科学普及中心）；SGT University（SGT大学）；Wroclaw University of Science and Technology（弗罗茨瓦夫科技大学）；Kharkov V.N. Karazin National University（哈尔科夫V.N.卡拉津国立大学）
A `resolution' of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machinery of Abstract Differential Geometry (ADG) is employed via Sorkin's finitary (:locally finite) poset substitutes of continuous manifolds in their Gel'fand-dual picture in terms of discrete differential incidence alg…
The foundations are laid for the numerical computation of the actual worldline for a particle orbiting a black hole and emitting gravitational waves. The essential practicalities of this computation are here illustrated for a scalar particle of infinitesimal size and small but finite scalar charge. This particle deviates from a geodesic because it interacts with its own retarded field $ψ^\ret$. A recently introduced Green's function $G^\SS$ precisely determines the singular part, $ψ^\SS$, of the retarded field. This part exerts no force on the particle. The remainder of the field $ψ^\R = ψ^\re…
We analyze the entanglement degradation provoked by the Hawking effect in a bipartite system Alice-Rob when Rob is in the proximities of a Schwarzschild black hole while Alice is free falling into it. We will obtain the limit in which the tools imported from the Unruh entanglement degradation phenomenon can be used properly, keeping control on the approximation. As a result, we will be able to determine the degree of entanglement as a function of the distance of Rob to the event horizon, the mass of the black hole, and the frequency of Rob's entangled modes. By means of this analysis we will s…
We use the phenomenological approach to study properties of space-time in the vicinity of the Schwarzschild black-hole singularity. Requiring finiteness of the Schwarzschild-like metrics we come to the notion of integrable singularity that is, in a sense, weaker than the conventional singularity and allows the (effective) matter to pass to the white-hole region. This leads to a possibility of generating a new universe there. Thanks to the gravitational field of the singularity, this universe is already born highly inflated ('singularity-induced inflation') before the ordinary inflation starts.
Retrieving the mass of a gravitational-wave (GW) source is a fundamental but difficult problem because the mass is degenerate with redshift. In astronomy, three types of redshift exist, namely cosmological, Doppler, and gravitational redshift, but the latter two are normally too weak to affect the observation. In this Letter, we show that the current astrophysical models allow binary black holes (BBHs) to merge within $10$ Schwarzschild radii of a supermassive black hole (SMBH). We find that in this case both the Doppler and gravitational redshift are significant, and in the most extreme condi…
Periodic orbits and gravitational waveforms around a Schwarzschild black hole with a cloud of strings embedded in perfect fluid dark matter
College of Physics, Guizhou University（贵州大学物理学院）；Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台）；College of Physics and Science and Technology, Hebei University（河北大学物理科学与技术学院）
Plasma impact on black hole shadow and gravitational weak lensing for Schwarzschild-like black hole
Harbin Institute of Technology（哈尔滨工业大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；New Uzbekistan University（新乌兹别克斯坦大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）
