arXiv subjects

Vladimir Dzhunushaliev

Publications and source records attributed to Vladimir Dzhunushaliev.

At least 19 recordsLinked to original sources

arXiv2026

Dirac stars in modified $F(R)$ gravity

We study Dirac mini-stars in modified $R^2$ gravity, where gravity is sourced by both linear and nonlinear spinor fields. Two-dimensional (2D) and three-dimensional (3D) profiles of the mini-star mass are constructed as functions of the spinor frequency (for the 2D profiles) and the central value of the spinor field (for the 3D profiles) in general relativity and modified gravity for various values of the spinor nonlinearity parameter. We show that the modification of gravity alters the properties of these configurations, while increasing the nonlinearity parameter within the framework of $R^2$ gravity significantly changes the profiles of the spinor and metric functions, the effective energy density, and the dependence of the total mass on the oscillation frequency. The most pronounced changes occur at large values of the nonlinearity parameter.

gr-qc↗

arXiv2026

Nonperturbative Dyson--Schwinger equations in QCD: a first approximation

We consider a procedure for nonperturbative quantization based on an infinite system of nonperturbative Dyson--Schwinger equations. We propose a first approximation for truncating this infinite system of equations in the static case. The main ideas underlying this approximation are as follows: (a) the two-point Green's functions of vacuum gauge fields are factorized by introducing scalar fields; (b) in the non-vacuum case, the degrees of freedom of the $SU(3)$ gauge field can be divided into ``almost classical'' and ``almost quantum'' degrees of freedom; (c) the four-point Green's functions of the gauge fields are represented as bilinear combinations of two-point Green's functions; (d) an approximation for the three-point Green's function describing the interaction between quarks and gauge fields is proposed, which leads to the splitting of the original Dirac equation for the quark-field operators into two equations, one describing the expectation value of the fermion field and the other acquiring a nonlinear term and serving to describe a condensate composed of sea quarks bound by the vacuum gauge field. We consider the choice of gauge appropriate for this approximation to nonperturbative quantization. We point out that the emergence of a nonlinear Dirac equation within this approximation may lead to a mass gap in the energy spectrum of solutions of the corresponding systems of equations. The issue of the emergence of ``dimensional transmutation'' within this approximation is also discussed. We provide arguments in favor of the statement that the ``closure constants'' appearing in the finite truncation and giving rise to ``dimensional transmutation'' should survive in the transition to the infinite system of Dyson--Schwinger equations. An analogy between nonperturbative quantization and the stochastic theory of turbulence is also discussed.

hep-th↗

arXiv2026

Non-Abelian monopoles in Einstein-scalar-Gauss-Bonnet gravity

We study static, spherically symmetric self-gravitating non-Abelian 't Hooft-Polyakov monopoles in Einstein-scalar-Gauss-Bonnet gravity for two classes of scalar-Gauss-Bonnet coupling functions. We demonstrate that the branch structure of the monopole solutions depends sensitively on the choice of the coupling function. For the polynomial coupling, we show that, for sufficiently large values of the coupling parameter, the principal part of the field equations becomes locally degenerate at a critical radius, leading to a critical solution that signals a geometric phase transition. By contrast, the exponential coupling acts as a natural regulator, preventing the degeneration of the principal part and preserving smooth field profiles. Finally, we discuss a possible physical interpretation of the critical solution, in which spacetime separates into an inner region where quantum-gravitational effects may become important and an outer region that remains well described by classical general relativity.

gr-qc↗

arXiv2026

Fermion condensate at the event horizon

Some arguments are considered in favor of the idea that the canonical anticommutation relations for fermions should be modified in curved spacetime near the event horizon of a black hole. Such a modification is expected to lead to a change in the source term of the inhomogeneous Dirac equation describing the two-point Green's function. By introducing an {\it ad hoc} source into the Dirac equation that mimics the modification of these anticommutation relations, stationary solutions are obtained and interpreted as two-point Green's functions of fermions located near the event horizon. Owing to their stationarity, these Green's functions describe a fermion condensate near the event horizon.

gr-qc↗

arXiv2026

Non-Abelian monopoles in modified gravity

Within modified gravity, we study static spherically and axially symmetric self-gravitating non-Abelian monopoles in $SU(2)$ Yang-Mills-Higgs theory. By comparing these monopoles with those obtained in Einstein-Yang-Mills-Higgs theory, we identify the differences introduced by the modification of gravity and show that they can be quite significant for systems with strong Higgs self-coupling.

hep-th↗

arXiv2026

Rotating wormholes in Einstein-Dirac-Maxwell theory

We consider rotating wormhole solutions in general relativity supported by a complex non-phantom spinor field (which provides a nontrivial spacetime topology) and electromagnetic fields. The solutions are asymmetric, regular, asymptotically flat and carry nonzero total angular momentum. The physical properties of the resulting configurations are completely determined by the values of three input quantities: the throat parameter, the spinor frequency, and the electromagnetic coupling constant. The wormholes connect two identical Minkowski spacetimes possessing in general different masses and global charges.

gr-qc↗

arXiv2026

Realistic classical charge from an asymmetric wormhole

Within Einstein-Dirac-Maxwell theory, we consider a wormhole solution supported by a complex non-phantom spinor field with a bare mass of the order of the Planck mass (which provides a nontrivial spacetime topology and an intrinsic angular momentum), an electric field (which provides a charge of the system), and a magnetic field. This solution describes an asymmetric wormhole connecting two different asymptotically flat spacetimes (two universes) in which there are in general different observed masses and charges. It is shown that, by suitably adjusting the values of free system parameters, at one end of the wormhole, one can obtain the values of the observed mass and charge typical of the Standard Model particles, whereas at the other end of the wormhole these physical quantities acquire the Planck values. Such a configuration incarnates Wheeler's idea of ``mass without mass'' and ``charge without charge'', and can be thought of as a model of a classical charge possessing a spin.

gr-qc↗

arXiv2026

Condensation of a spinor field at the event horizon

The physical effect of condensation of a classical spinor field at the event horizon is under consideration. The corresponding solution is sought for the set of the Einstein-Dirac equations. It is shown that in this case there arises a black hole with a $δ$-like classical spinor field concentrated at the event horizon.

gr-qc↗

arXiv2026

Color field configuration between three static quarks

Within Yang-Mills-Proca theory with external sources in the form of three static quarks, regular, finite energy solutions are obtained. It is shown that color electric/magnetic fields have two components: the first part is a gradient/curl component, respectively, and the second part is a nonlinear component. It is shown that the color electric field has a Y-like spatial distribution provided by three static quarks. Such a Y-like behavior arises because the gradient component of the electric field is present. The nonlinear component of the electric field is a curl one, and it appears because the vector potential sourced by a solenoidal current is present. The color magnetic field is purely curl one, since its nonzero color components do not contain a nonlinear component; this results in the fact that its force lines lie on the surface of a torus. It is shown that the results obtained are in satisfactory agreement with the results obtained in lattice calculations in quantum chromodynamics. To discuss such an agreement, we have shown that the Yang-Mills-Proca equation can be obtained from the Lagrangian describing a gluon condensate varying in space. Also, we compare the energy profile obtained by us with that obtained in lattice calculations with a static potential.

hep-lat↗

arXiv2026

Wormholes in Einstein-Dirac-Maxwell theory with identical spacetime asymptotics

Within general relativity, we study spherically symmetric configurations with wormhole topology consisting of spinor fields and a Maxwell electric field. For such a system, we construct complete families of regular asymmetric solutions describing wormholes connecting two identical Minkowski spacetimes. The physical properties of such systems are completely determined by the values of three input quantities: the throat parameter, the spinor frequency, and the coupling constant. Depending on the specific values of these parameters, the configurations may have essentially different characteristics, including negative ADM masses.

gr-qc↗

arXiv2025

Dirac stars with wormhole topology

We consider configurations consisting of a gravitating nonlinear spinor field and a massless ghost scalar field providing a nontrivial spacetime topology. For such a mixed system, we have constructed families of asymptotically flat asymmetric solutions describing Dirac stars with wormhole topology. The physical properties of such systems are completely determined by the values of three input quantities: the nonlinearity parameter of the spinor field, the spinor frequency, and the throat parameter. Depending on the specific values of these parameters, the configurations may be regular or singular and possess one or two throats, as well as they may contain possible horizons of different kinds. Furthermore, because of the asymmetry, masses and sizes of the configurations observed at the two asymptotic ends of the wormhole may differ considerably. For large negative values of the nonlinearity parameter, it is possible to obtain configurations whose masses are comparable to the Chandrasekhar mass and effective radii are of the order of kilometers.

gr-qc↗

arXiv2025

Fermions localized on $U(1)$ gauged Q-balls

The axially symmetric $U(1)$ gauged self-interacting Q-balls are shown to support normalizable fermionic bound state, minimally coupled to the electromagnetic field of the Q-ball. It is shown that the effects of the backreaction of the fermionic mode are very small. We explore the domain of existence of the solutions and address some of their physical properties. Among other properties, we observe that the eigenvalue of the Dirac operator remains positive, there is no zero mode in the spectrum.

hep-th↗

arXiv2024

Gravitating Skyrmions with localized fermions

We consider self-gravitating Skyrmions in the presence of Dirac fermions, that carry spin and isospin. By varying the gravitational and the Yukawa coupling constants, we investigate the spectral flow of the fermion eigenvalue associated with a zero mode in the absence of gravity. We demonstrate that the backreaction of the fermion can strongly influence the Skyrmion-fermion configurations. In particular, the energy conditions may be violated, and regular anti-gravitating asymptotically flat solutions with negative ADM mass may emerge.

hep-th↗

arXiv2024

Fermion states localized on a self-gravitating Skyrmion

We investigate self-gravitating solutions of the Einstein-Skyrme theory coupled to spin-isospin Dirac fermions and consider the dependence of the spectral flow on the effective gravitational coupling constant and on the Yukawa coupling. It is shown that the effects of the backreaction of the fermionic mode may strongly deform the configuration. Depending on the choice of parameters, solutions with positive, negative and zero ADM mass may arise. The occurrence of regular anti-gravitating asymptotically flat solutions with negative ADM mass is caused by the violation of the energy conditions.

hep-th↗

arXiv2024

Chromoelectric flux tubes within non-Abelian Proca theory

Flux tube solutions within non-Abelian SU(3) Proca theory with external sources are obtained. It is shown that such tubes have a longitudinal chromoelectric field possessing two components (nonlinear and gradient), as well as a transverse chromomagnetic field whose force lines create concentric circles with the center on the axis of the tube. The scenario of a possible relationship between non-Abelian Proca theory and quantum chromodynamics is considered. In such scenario: (a)~the components of color fields have different behavior: those which are almost classical, and those which are purely quantum; (b)~the second components create a gluon condensate that is a source of the field for the almost classical components of the Proca field; (c)~Proca masses may appear as a result of an approximate description of the gluon condensate; (d)~the question of gauge invariance is considered. It is shown that the results obtained are in good agreement with the results of lattice calculations. We make an assumption that an approximate description of a flux tube in quantum chromodynamics can be carried out using classical Proca equations but with a mandatory account of a gluon condensate.

hep-th↗

arXiv2023

Quantum measure as a necessary ingredient in quantum gravity and modified gravities

We suggest commutation relations for a quantum measure. In one version of these relations, the right-hand side takes account of the presence of curvature of space; in the simplest case, this yields the action of general relativity. We consider the cases of the quantization of the measure on spaces of constant curvature and show that in this case the commutation relations for the quantum measure are analogues of commutation relations in loop quantum gravity. It is assumed that, in contrast to loop quantum gravity, a triangulation of space is a necessary trick for quantizing such a nonlocal quantity like a measure; in doing so, the space remains a smooth manifold. We consider the self-consistent problem of the interaction of the quantum measure and classical gravitation. It is shown that this inevitably leads to the appearance of modified gravities. Also, we consider the problem of defining the Euler-Lagrange equations for a matter field in the background of a space endowed with quantum measure.

gr-qc↗

arXiv2023

Charged spinning fermionic configurations and a mass gap

We consider a self-consistent axially symmetric system supported by a classical nonlinear spinor field minimally coupled to electric and magnetic Maxwell fields. The presence of the nonlinearity of the spinor field ensures the existence of a minimum positive energy of the system (a mass gap), of a minimum charge (a charge gap), and of a minimum magnetic moment. In turn, the presence of the electric charge results in qualitative changes in the behavior of physical characteristics of the systems under consideration as compared with the case of an electrically neutral spinor field. It is shown that, with a suitable choice of free system parameters, there exists a regular finite-energy particlelike solution describing a localized spinning object whose physical parameters correspond to the main characteristics of an electron/positron (including the spin equal to $1/2$), but with the characteristic size comparable to the corresponding Compton wavelength. Also, we show that four local Dirac equations are equivalent to two nonlocal equations.

hep-th↗

arXiv2023

Fermion states localized on a self-gravitating non-Abelian monopole

We study fermionic modes localized on the static spherically symmetric self-gravitating non-Abelian monopole in the $SU(2)$ Einstein-Dirac-Yang-Mills-Higgs theory. We consider dependence of the spectral flow on the effective gravitational coupling constant and show that, in the limiting case of transition to the Reissner-Nordström black hole, the fermion modes are fully absorbed into the interior of the black hole.

hep-th↗