arXiv subjects

M. V. Gorbatenko

Publications and source records attributed to M. V. Gorbatenko.

At least 19 recordsLinked to original sources

arXiv2020

Quantum mechanics of stationary states of particles in a space-time of classical black holes

We consider interactions of scalar particles, photons, and fermions in Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman gravitational and electromagnetic fields with a zero and nonzero cosmological constant. We also consider interactions of scalar particles, photons, and fermions with nonextremal rotating charged black holes in a minimal five-dimensional gauge supergravity. We analyze the behavior of effective potentials in second-order relativistic Schrödinger-type equations. In all cases, we establish the existence of the regime of particle "falling" on event horizons. An alternative can be collapsars with fermions in stationary bound states without a regime of particles "falling".

physics.gen-ph↗

arXiv2020

Quantum mechanics of stationary states of particles in external singular spherically and axially symmetric gravitational and electromagnetic fields

The report considers the interaction of scalar particles, photons and fermions with the gravitational and electromagnetic Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman fields. The behavior of effective potentials in the relativistic Schrödinger-type second-order equations is analyzed. It was found that the quantum theory is incompatible with the hypothesis of the existence of classical black holes with event horizons of zero thickness that were predicted based on solutions of the general relativity (GR) with zero and non-zero cosmological constant $Λ$. The alternative may be presented by compound systems, i.e., collapsars with fermions in stationary bound states.

physics.gen-ph↗

arXiv2020

Comparison of conformal gravitation theories by solutions analogous to Reissner-Nordström ones

An exact solution was produced for one of the versions of conformal -invariant gravitation theories (conformal geometrodynamics - CG) for the body with a mass and an electric charge. The solution is analogous to the Reissner-Nordström solution in the general relativity theory. Its similar solution was earlier produced by Mannheit and Kazanas for the different version of the conformal-invariant gravitation theory -- Weyl conformal gravitation theory (Weyl CGt). Similar solutions do not comply. Issues of conformity with regard to the similar solutions are discussed. A conclusion is made that only the similar solution produced from conformal geometrodynamics (CG) equations corresponds to electrodynamic equations.

gr-qc↗

arXiv2019

Quantum mechanical equivalence of the metrics of a centrally symmetric gravitational field

We analyze the quantum mechanical equivalence of the metrics of a centrally symmetric uncharged gravitational field. We consider the static Schwarzschild metric in spherical and isotropic coordinates, the stationary Eddington-Finkelstein and Painlevé-Gullstrand metrics, and nonstationary Lemaître-Finkelstein and Kruskal-Szekeres metrics. When the real radial functions of the Dirac equation and of the second-order equation in the Schwarzschild field are used, the domain of wave functions is restricted to the range $r>r_{0}$, where $r_{0}$ is the radius of the event horizon. A corresponding constraint also exists in other coordinates for all considered metrics. For the considered metrics, the second-order equations admit the existence of degenerate stationary bound states of fermions with zero energy. As a result, we prove that physically meaningful results for a quantum mechanical description of a particle interaction with a gravitational filed are independent of the choice of a solution for the centrally symmetric static gravitational field used.

physics.gen-ph↗

arXiv2017

The Mannheim-Kazanas solution, the conformal geometrodynamics and the dark matter

Within the framework of the Einstein's standard equations of the general theory of relativity, flat galactic rotational curves of galaxies cannot be explained without hypothesis attracting the dark matter, the particles of which had not yet been identified. The vacuum central-symmetric solution of the equations of conformal gravitation is well known as metrics of Mannheim-Kazanas, on the basis of which these curves receive purely geometrical explanation. We show in our work that the metrics of Mannheim-Kazanas is the solution of not only Bach equations received from conformal-invariant Weyl Lagrangian, but also the solution of equations of the conformal geometrodynamics at a nonzero vector of Weyl. In this connection the hypothesis is formulated that the space on galactic scales can be described not only by Riemannian geometry, but with geometry of Weyl.

gr-qc↗

arXiv2017

Stationary bound states of spin-half particles in the Reissner-Nordstroem gravitational field

We prove the possibility of existence of stationary bound states of spin-half particles in the Reissner-Nordstroem gravitational field using a self-conjugate Hamiltonian with a flat scalar product of wave functions. Bound states of Dirac particles with a real discrete energy spectrum can exist both for particles above the external "event horizon", and for particles under the internal "event horizon", or the Cauchy horizon. The Hilbert condition g_{00}>0 leads to a boundary condition such that components of the vector of current density of Dirac particles are zero near the "event horizons". Based on the results of this study, we can assume that there exists a new type of charged collapsars, for which the Hawking radiation is not present. The results of this study can lead to a revision of some concepts of the standard cosmological model related to the evolution of the universe and interaction of charged collapsars with surrounding matter.

gr-qc↗

arXiv2017

Stationary bound states of spin-half particles in the Kerr and Kerr-Newman gravitational fields

We prove the possibility of existence of stationary bound states of stationary bound states of spin-half probe particles for the Kerr and Kerr-Newman gravitational fields using Chandrasekhar's Hamiltonian. If the Hilbert condition is satisfied, g_{00}>0, bound states of Dirac particles with a real discrete energy spectrum can exist both for particles outside the surface of the outer ergosphere of the Kerr and Kerr-Newman fields, and for particles under the surface of the inner ergosphere. In this case, the surfaces of the external and internal ergospheres play the role of infinitely high potential barriers. Spin-half quantum-mechanical particles cannot cross the ergosphere surfaces of the Kerr and Kerr-Newman fields. Based on the results of this study, we can assume that there exists a new type of rotating collapsars, for which the Hawking radiation is absent. The results of this study can lead to a revision of some concepts of the standard cosmological model related to the evolution of the universe and interaction of rotating collapsars with surrounding matter.

gr-qc↗

arXiv2015

Cosmic censorship and stationary states of half-spin particles in the field of Reissner-Nordstroem naked singularity

The paper explores quantum mechanics of half-spin particle motion in the field of Reissner-Nordstroem (RN) naked singularity. It is shown that for any quantum mechanical Dirac particle, irrespective of availability and sign of its electrical charge, the RN naked singularity is separated by an infinitely high positive potential barrier. With like charges of a particle and the source of the RN naked singularity, near the origin there exists the second completely impenetrable potential barrier. It has been proved that in the field of the RN naked singularity, bound states of half-spin particles can exist. The conditions for appearance of such states were revealed and computations were performed to find energy eigenvalues and eigenfunctions.

gr-qc↗

arXiv2015

Analysis of half-spin particle motion in Reissner-Nordstroem and Schwarzschild fields by means of the method of effective potentials

The paper presents the analysis of effective potentials of Dirac equations in Schwarzschild and Reissner-Nordstroem fields. It is shown that in the majority of the explored cases the condition of a particle "fall" to appropriate event horizons is fulfilled. The exception is one of the solutions with normalizable wave functions for the Reissner-Nordstroem extreme field, for which the existence of the stationary bound state of half-spin particles is possible inside the event horizon.

gr-qc↗

arXiv2015

Some Aspects of Quantum Mechanics of Particle Motion in Static Centrally Symmetric Gravitational Fields

The domain of wave functions and effective potentials of the Dirac and Klein-Gordon equations for quantum-mechanical particles in static centrally symmetric gravitational fields are analyzed by taking into account the Hilbert causality condition. For all the explored metrics, assuming existence of event horizons, the conditions of a "fall" of a particle to the appropriate event horizons are implemented. The exclusion is one of the solutions for the Reissner-Nordstroem extreme field with the single event horizon. In this case, while fulfilling the condition found by V.I.Dokuchaev, Yu.N.Yeroshenko, the normalization integral is convergent and the wave functions become zero on the event horizon. This corresponds to the Hilbert causality condition. In our paper, due to the analysis of the effective potential for the Reissner-Nordstroem extreme field with real radial wave functions of the Dirac equation, the impossibility is demonstrated for the bound stationary state existence of quantum-mechanical particles, with positive energy, off the event horizon. The analysis of the effective potential of the Dirac equation for the case of the naked singularity of the Reissner-Nordstroem field shown the possible existence of stationary bound states of quantum-mechanical half-spin particles.

gr-qc↗

arXiv2014

Analysis of the quantum-mechanical equivalence of the metrics of a centrally symmetric uncharged gravitational field

In the paper we analyze the quantum-mechanical equivalence of the metrics of a centrally symmetric uncharged gravitational field. We consider the Schwarzschild metrics in the spherical, isotropic and harmonic coordinates, and the Eddington-Finkelstein, Painleve-Gullstrand, Lemaitre-Finkelstein, Kruskal metrics. The scope of the analysis includes domains of the wave functions of Dirac's equation, hermiticity of Hamiltonians, and the possibility of existence of stationary bound states of spin-half particles. The constraint on the domain of the wave functions of the Hamiltonian in a Schwarzschild field in spherical coordinates (r > r_{0}) resulting from the fulfillment of Hilbert's condition g_{00} > 0 also holds in other coordinates for all the metrics considered. The self-adjoint Hamiltonians for the Schwarzschild metrics in the spherical, isotropic and harmonic coordinates and also for the Eddington-Finkelstein and Painleve-Gullstrand metrics are Hermitian, and for them the existence of stationary bound states of spin-half particles is possible. The self-adjoint Hamiltonians for non-stationary Lemaitre-Finkelstein and Kruskal metrics have the explicit dependence on the temporal coordinates and stationary bound states of spin-half particles cannot be defined for these Hamiltonians. The results of this study can be useful when addressing the issues related to the evolution of the universe and interaction of collapsars with surrounding matter.

gr-qc↗

arXiv2014

A Modified Method for Deriving Self-Conjugate Dirac Hamiltonians in Arbitrary Gravitational Fields and Its Application to Centrally and Axially Symmetric Gravitational Fields

We have proposed previously a method for constructing self-conjugate Hamiltonians H_eta in the eta-representation with a flat scalar product to describe the dynamics of Dirac particles in arbitrary gravitational fields. In this paper, we prove that, for block-diagonal metrics, the Hamiltonians H_eta can be obtained, in particular, using "reduced" parts of Dirac Hamiltonians, i.e. expressions for Dirac Hamiltonians derived using tetrad vectors in the Schwinger gauge without or with a few summands with bispinor connectivities. Based on these results, we propose a modified method for constructing Hamiltonians in the eta-representation with a significantly smaller amount of required calculations. Using this method, here we for the first time find self-conjugate Hamiltonians for a number of metrics, including the Kerr metric in the Boyer-Lindquist coordinates, the Eddington-Finkelstein, Finkelstein-Lemaitre, Kruskal, Clifford torus metrics and for non-stationary metrics of open and spatially flat Friedmann models.

gr-qc↗

arXiv2014

Equivalence and Hermiticity of Dirac Hamiltonians in the Kerr gravitational field

In the paper, for the Kerr field, we prove that Chandrasekhar's Dirac Hamiltonian and the self-adjoint Hamiltonian H_η with a flat scalar product of the wave functions are physically equivalent. Operators of transformation of Chandrasekhar's Hamiltonian and wave functions to the η-representation with a flat scalar product are defined explicitly. If the domain of the wave functions of Dirac's equation in the Kerr field is bounded by two-dimensional surfaces of revolution around the z axis, Chandrasekhar's Hamiltonian and the self-adjoint Hamiltonian in the η-representation are Hermitian with equality of the scalar products,(ψ, H φ)=(H ψ, φ).

gr-qc↗

arXiv2013

Quantum-mechanical nonequivalence of metrics of centrally symmetric uncharged gravitational field

Quantum-mechanical analysis shows that the metrics of a centrally symmetric uncharged gravitational field, which are exact solutions of the general relativity equations, are physically non-equivalent. The classical Schwarzschield metric and the Schwarzschild metrics in isotropic and harmonic coordinates provide for the existence of stationary bound states of Dirac particles with a real energy spectrum. The Hilbert condition g_{00}>0 is responsible for zero values of the wave functions under the "event horizon" that leads to the absence of Hawking radiation. For the Eddington-Finkelstein and Painleve-Gullstrand metrics, stationary bound states of spin-half particles cannot exist because Dirac Hamiltonians are non-Hermitian. For these metrics, the condition g_{00}>0 also leads to the absence of Hawking evaporation. For the Finkelstein-Lemaitre and Kruskal metrics, Dirac Hamiltonians are explicitly time-dependent, and stationary bound states of spin-half particles cannot exist for them. The Hilbert condition for these metrics does not place any constraints on the domains of the wave functions. Hawking evaporation of black holes is possible in this case. The results can lead to revisiting some concepts of the standard cosmological model related to the evolution of the universe and interaction of collapsars with surrounding matter.

gr-qc↗

arXiv2013

Stationary Bound States of Dirac Particles in the Schwarzschild Gravitational Field

Nondecaying bound states of elementary spin-half particles are validated and calculated numerically for the Schwarzschild gravitational field using a self-conjugate Hamiltonian with a flat scalar product for any value of the gravitational coupling constant. Hilbert condition g_{00}>0 leads to a boundary condition such that components of the vector of current density of Dirac particles are zero near the "event horizon". At small values of the coupling constant, the energy spectrum is close to the hydrogen-like spectrum. Based on the results of this study, we can assume that there exists a new type of collapsars, for which the Hawking radiation mechanism is not present. From the standpoint of cosmology, if the value of the gravitational coupling constant is small, alpha<<1, the new type of nonradiating relict collapsars can manifest itself only through gravitation. Thus, they are good candidates for the role of "dark matter" carriers. In the wide range of admissible masses, there can exist collapsars of a new type with the masses of hypothesized WIMP particles, which are treated as representatives of "dark matter" in numerous scenarios of the expansion of the universe. The results of this study can lead to revisiting some concepts of the standard cosmological model related to the evolution of the universe and interaction of collapsars with surrounding matter.

gr-qc↗

arXiv2013

Stationary Bound States of Dirac Particles in Collapsar Fields

Stationary bound states of elementary spin 1/2 particles that do not decay with time are obtained for a Schwarzschild gravitational field using a self-conjugate Hamiltonian with a flat scalar product at small values of gravitational coupling constant. In order to obtain a discrete energy spectrum, we introduce a boundary condition such that the azimuthal current density of Dirac particles on the "event horizon" is zero. The results can lead to revisiting some concepts of the standard cosmological model related to the evolution of the universe and interaction of collapsars with surrounding matter.

gr-qc↗

arXiv2013

Absence of the non-uniqueness problem of the Dirac theory in a curved spacetime. Spin-rotation coupling is not physically relevant

As opposed to Arminjon statements, in this work we again assert the absence of the non-uniqueness problem of the Dirac theory in a curved and flat spacetime and illustrate this with a number of examples. Dirac Hamiltonians in arbitrary, including time-dependent, gravitational fields uniquely determine physical characteristics of quantum-mechanical systems irrespective of the choice of the tetrad fields. Direct spin-rotation coupling that occurs with a certain choice of tetrads does not manifest itself in final physical characteristics of the systems and therefore does not represent a physically relevant effect.

gr-qc↗

arXiv2011

Atoms and Forces of Interaction Between Elementary Particles in the Expanding Universe

The earlier developed algorithm for constructing a self-conjugate Hamiltonian in the η-representation for Dirac particles interacting with a general gravitational field is extended to the case of electromagnetic fields. This Hamiltonian is applied to the case when the gravitational field describes the spatially flat Friedmann model, and the electromagnetic field is the Coulomb potential extended to the case of this model. The analysis of atomic systems and electromagnetic forces of interaction under the conditions of spatially flat expansion of the universe has demonstrated that the system of atomic levels does not change with cosmological time. Spectral lines of atoms in the spatially flat Friedmann model are identical at different points of cosmological time. In this case the redshift is stipulated entirely by the growth of wavelength of photons at movement in the expending universe. At the same time force of interaction between elementary particles can change with expansion of the universe.

gr-qc↗