Гравитация, космология и фундаментальные поля. Рубрика в журнале - Пространство, время и фундаментальные взаимодействия
A moving black hole in TEGR as a moving matter ball
Статья научная
Possibilities of the covariant with respect to both coordinate and local Lorentz transformations formalism developed earlier in the framework of Teleparallel Equivalent of General Relativity (TEGR) are studied. The formalism is applied to a solution for a moving with constant velocity (with respect to distant static observers) Schwarzschild black hole. Coordinate and Lorentz invariant global conserved mass and momentum are constructed. The acceptable results are obtained in spite of the solution under consideration has no, at least, Killing vectors of space displacements. Calculations are quite analogous to calculating the mass and momentum of a moving matter ball in Minkowski space, and this analogy is used essentially.
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About leptons in space-time film theory
Статья научная
In the present work, we continue the investigation of the problem for finding the toroidal soliton solutions of space-time film equation, which can represent the charged leptons. The quasi-cylindrical complex toroidal coordinate system with rotation is introduced and the appropriate equation of space-time film is obtained. We propose the way for finding the solutions in the form of formal series in negative powers of the radius of the toroidal ring. The initial approximation for this method is discussed.
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Application of the Schrodinger equation in exact scalar field cosmology
Статья научная
We propose a new method of exact solutions construction for scalar field cosmology based on representation of the Einstein-Friedmann dynamic equations as Schr¨odinger-like one. This representation allows one to compare the solutions of quantum-mechanical and cosmological problems. On the other hand, this approach makes it possible to use the well-known form-invariant transformations of the Schr¨odinger equation to generate exact cosmological solutions. As an example of the application of this method, the use of the Darboux transformations in scalar field cosmology is considered. On the other hand, the presented methods make it possible to generalize the obtained solutions to multi-field cosmological models.
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Black holes and the nature of the event horizon
Статья научная
The problem of the event horizon in relativistic gravity is discussed. Singular solutions in general relativity are well known. The Schwarschild metric of a spherical mass is singular at zero (𝑟 = 0) and at the event horizon (𝑟 = 𝑟𝑔). Both features reflect the existence of the phenomenon of collapse in general relativity for compact masses exceeding 3𝑀⊙. A material particle crossing the event horizon falls into a central singularity according to the classical theory of general relativity. In the quantum theory of gravity, there may be no central singularity. The physics of the event horizon is currently being refined. A promising technique is the study of gravitational waves (GW) accompanying the merger of binary black holes at the ringdown stage. GW observations of quasinormal modes of the newly formed super dense remnant will help clarify the physics of the event horizon.
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Bouncing cosmology in modified theories of gravity
Статья научная
In this study, we describe a 𝑓(𝑅) gravity theory-based bouncing cosmological model of the universe. The flat FLRW space-time were used to determine the model’s dynamical behaviour. At the bouncing epoch, the geometrical parameters exhibit singularity behaviour. The parameters of the scale factor have a significant impact on the bouncing behaviour.
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Cамодействие скалярного заряда в заряженной экстремальной анти-дилатонной кротовой норе
Статья научная
Вычислена сила самодействия скалярного заряда в пространство-времени экстремальной заряженной анти-дилатонной кротовой норы. Предполагается, что скалярный заряд является источником безмассо- вого скалярного поля, минимально связанного с кривизной пространства-времени.
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Detectors of high-frequency gravitational waves based on the gravitational-optical resonance
Статья научная
In this paper, we consider the possibility of registering relic gravitational waves predicted in cosmological models of the early universe with an additional stage of stiff energy dominance. Differences in the spectrum of relic gravitational waves in these models from the case of standard inflationary models are considered. A method for detecting high-frequency gravitational waves based on gravitational-optical resonance in Fabry-Perot interferometers is proposed. The main parameters of the detector are calculated and the frequency range of relic gravitational waves, which can be registered using the proposed approach, is determined.
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Dynamo-optically active media: new aspects of the Minkowski-Abraham controversy
Статья научная
Based on the covariant variation formalism, two versions of the symmetric effective stress-energy tensor of the electromagnetic field in a dynamo-optically active relativistic media are reconstructed in the framework of the tetrad and aether paradigms, respectively. We show that the energy density scalars and pressure tensors coincide for both versions of the stress-energy tensors, however, the corresponding energy flux four-vectors happen to be different in general case. This mathematical fact adds new arguments into the 100-year-long discussion, which is called Minkowski-Abraham controversy and is connected with the correct definition of the electromagnetic energy flux in a continuous media. We consider three examples: first, the axionically active vacuum; second, the spatially isotropic moving dielectric medium; third, the dynamo-optically active medium. We discuss possible applications of the elaborated formalism.
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Electron scattering on a wormhole in the Born approximation
Статья научная
The wormholes which connect either two distant regions of the same Universe or two universes are one of the intriguing hypothetical objects in the physics of gravitational interaction. For wormholes to be traversable, i.e., to allow a traveler to cross them safely, the wormholes must be filled with exotic matter within the framework of general relativity. In this paper it is shown that under certain conditions the number of electrons elastically scattered on an Ellis-Bronnikov wormhole exceeds the number of electrons of the incident flux. The additional electrons appear as a result of their transition through the wormhole from the opposite side of the catenoid. In other words, a negative pressure is created in the wormhole by means of the flux of electrons directed to the wormhole. This allows us to conclude that the wormhole can be stabilized without exotic matter in this way.
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Exact solutions in Friedmann cosmology with scalar fields
Статья научная
The method of exact analysis of cosmological dynamics at the early inflation stage of the evolution of the Friedman Universe, which is determined by the dynamics of the scalar field for the case of minimal and nonminimalinteraction of the field and curvature is considered in this work. The basis of the method is to reduce theequations of dynamics to the same form for all models. The proposed approach allows us to compare modelsbased on the different theories of gravity.
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Exact solutions in modified gravity theories
Статья научная
In this paper, we have reviewed the limitations in the General Relativity theory and the requirement for geometrical dark energy models. Actions for different geometrical dark energy models have been discussed. Specifically, two matter geometry coupling models within the Einstein-Hilbert action have been investigated. The basic equations leading to the discussion of the dynamical aspects of the Universe are derived and some examples of obtaining exact solutions in these two models are discussed.
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Статья научная
The problem reduction of an evolution modelling of the open Universe for conformally flat space-time metric in Fock’s form to an equivalent problem of a particle movement with an unit mass in a force field is demonstrated. The exact cosmological models filled with a substance and radiation in an approximation of the perfect fluid are found since the Friedman solution by means an introduction of set "mechanical" potentials.In the article the possibility of deriving from the Einstein equations exact cosmological solutions for the open Universe by reduction to the equivalent problem of a mass particle motion in the force field is considered. The cosmological model is filled by substance in an approximation of the perfect fluid with nonzero pressure, generally speaking. The metric of 4D space-time is taken in the Fock form as the metric conformal to the Minkowski metric. This metric has the dependence on one variable. A square of the variable is product of advanced and retarded times.The using of mechanical interpretation of the gravitation equations leads to a possibility of consideration of various mechanics force fields with the subsequent physical interpretation of the found exact cosmological solutions.First of all a movement of a free particle with an unit mass (a mechanical force equals to zero) is considered,i.e. the particle moves on inertia. The fourth degree of discovered law of movement is a conformal factor of the cosmological metric which is conformally flat. This case corresponds to the exact cosmological solution without pressure, coinciding with known the Friedman solution for the open Universe.After that the force field leading to uniformly decelerated motion of a particle is considered. The force potential is taken in the form of linear function. The tangent of a slope angle of the function curve coincides with particle acceleration. Such research leads to the exact cosmological solution asymptotically describing both an incoherent dust, and the ultrarelativistic substance which may be interpreted as an equilibrium radiation.Further a square-law function without a linear term and a constant value is taken as a force potential. Such potential can be interpreted as potential of the free oscillator. The solution of corresponding equation of motion is written down in the form of a cosine function with some initial phase related to the ratio between parameters which define dust-like and ultrarelativistic substance. This conclusion becomes obvious after concidering asymptotic behaviour of pressure and energy density. Besides, the series expansion of a root of the fourth degree from a conformal factor asymptoticly coincides with the law of uniformly decelerated motion in previous case that indicates its particular character.
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Extended relativistic non-equilibrium thermostatics of stellar structures with radiation pressure
Статья научная
We establish the extended formalism for description of the static spherically symmetric relativistic non-equilibrium stellar systems in the formation of which the radiation pressure plays the key role. The main concept of this extended formalism inherits the ideas, on which the Israel-Stewart causal thermodynamics is based, but now the unit spacelike four-vector, indicated by the term director, is exploited in addition to the unit timelike medium velocity four-vector. An application of the extended formalism is considered; we analyze the profiles of the non-equilibrium pressure and temperature as the functions of guiding parameters introduced phenomenologically.
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Extragalactic TEV photons and the zero-point vibration spectrum limit
Статья научная
There are observations indicating a possible anomalous transparency of intergalactic space (filled with infrared background light) for extragalactic gamma-rays of very high energy (> 100 GeV). The anomaly is usually associated with effects of some new physics. However, another explanation is possible - as a manifestation relating to a cut-off of the zero-point vibration spectrum. It is assumed that this boundary 𝑈ZV is isotropic in the reference frame, where the cosmic microwave background (CMB) radiation is isotropic, and an estimate is obtained: 𝑈ZV ≈ 7.4TeV. It is noted that the presence of a boundary also leads to an increased beta decay time of accelerated particles with the Lorentz factor > 50 (in the CMB rest frame; in addition to the usual (𝛽)). It is widely believed that the ZV-spectrum continues up to the Planck energy (in natural units, the gravitational constant is related to the square of the Planck length). There is, however, a 5D variant of the Absolute Parallelism theory (AP), free from singularities of solutions, where a large characteristic length appears, which determines the thickness of expanding spherical 𝑆3 shell (a cosmological solution as the longitudinal wave along the radius) in co-moving co-ordinates. Newton’s Law ~ 1/𝑟2 is replaced by 1/𝑟 at distances exceeding 𝐿, and the Planck length (a composite parameter) “arises” from when switching to the conventional energy-momentum scale (where the energy of a photon is its angular frequency). The theory features are briefly exposed - description of 15 polarizations (degrees of freedom), the energymomentum tensor (in prolonged 4th order equations), topological charges and quasi-charges of localized field configurations.
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Статья научная
The paper presents a some specific method of the gravitational frequency shift measurement for communication radio signals between the spacecraft and ground tracking stations. It is based on the maximum likelihood algorithm and utilizes the Cram´er-Rao bound to estimate the accuracy of signal parameter determination. It is carried out with the bank of data obtained during the “Radioastron” mission. Attention is concentrated at a compensation of the relativistic Doppler effect and frequency noises of the standards used in the experiment
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Generalization of the C3 matching procedure
Статья научная
To handle the case in which discontinuities are present along the matching hypersurface, in this work, we present a generalization of the 𝐶3 matching procedure discussed in previous works. It demands that a solution of Einstein’s equations also describe the matching hypersurface.
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Generalized Kaluza-Klein models with Gauss-Bonnet lagrangians
Статья научная
The five-dimensional generalization of Einstein’s theory of gravitation proposed first by Th. Kaluza (1921) and improved a few years later by O. Klein (1926) has led to the Kaluza-Klein model incorporating electromagnetism and gravitation, and a variant of the Brans-Dicke theory of gravity, containing a scalar field interacting with metric tensor field. However, neither of these models did use the possibilities offered by the enlargement of the Einstein-Hilbert variational principle via including the Gauss-Bonnet invariant, which in 5 dimensions is no more a pure divergence, and modifies substantially the equations of motion of the theory. After recalling the basics of the Kaluza-Klein model, including the non-abelian case. we give a short review of multi-dimensional cosmological models with scalar fields generated by gauge fields defined on the structural group, including the generalized lagrangian containing the Gauss-Bonnet term 𝑅𝐴𝐵𝐶𝐷𝑅𝐴𝐵𝐶𝐷-4𝑅𝐴𝐵𝑅𝐴𝐵+𝑅2. Then we turn our attention back to the 5-dimensional Kaluza-Klein model, without scalar field and neglecting gravity, but with variational principle enriched by the Gauss-Bonnet term, This leads, in the Minkowskian space-time, to an interesting variant of non-linear Electrodynamics. After discussing the modified Maxwell’s equations, we show how a toroidal soliton can be constructed, and show that it displays the most essential features of Dirac’s electron: electric charge, magnetic moment, and spin. It also predicts the particle-anti particle symmetry.
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H-spaces (H41,G) of type {41}: projective-group properties
Статья научная
In this paper we study five-dimensional ℎ-spaces (𝐻41, 𝑔) of type {41} [4]. Necessary and sufficient conditions for (𝐻41, 𝑔) to be a space of constant curvature are found. The general solution of the Eisnhart equation in ℎ-space (𝐻41, 𝑔) of non-constant curvature is determined. We establish conditions for the existence of a non-homothetic projective motion in (𝐻41, 𝑔) and describe the structure of a non-homothetic projective Lie algebra in ℎ-space (𝐻41, 𝑔) of type {41}.
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Статья обзорная
В данной статье представлен обзор работы III летней международной молодежной школы «Гравитация, космология и астрофизика», посвященной памяти академика РАН В.И. Пустовойта.
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Inflationary models based on generalized exact cosmological solutions
Статья научная
This paper proposes a method for constructing an unlimited number of exact solutions to the equations of cosmological dynamics for the case of Einstein gravity and the teleparallel equivalent of general relativity. The exact cosmological solutions obtained within the framework of this approach imply complex types of evolution of the scalar field and the dynamics of the expansion of the universe. As an example, solutions to the equations of cosmological dynamics in the form of series are considered, each term of which and the entire series are exact solutions. It is shown that with a certain choice of parameters, the solutions obtained correspond to the correct dynamics of the expansion of the universe at various stages of its evolution
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