arXiv subjects

Vladimir Folomeev

Publications and source records attributed to Vladimir Folomeev.

At least 19 recordsLinked to original sources

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↗

arXiv2024

Wormholes inside stars and black holes

We construct models of two exotic objects: (i) a wormhole whose throat is hidden by a stellar object like a neutron star; and (ii) a wormhole inside a black hole. We work within Einstein's gravity coupled to two scalar fields with a specific choice of the scalar field Lagrangian. In general, the model contains ghosts, but they are eliminated using the constraints given by the Lagrange multiplier fields. The constraints are a generalization of the mimetic constraint, where non-dynamical dark matter effectively appears. As a result, in our model, instead of the non-dynamical dark matter, non-dynamical exotic matter like a phantom effectively arises. For the mixed wormhole-plus-star system, we find the corresponding mass-radius relations and show that it is possible to get characteristics comparable to those of ordinary neutron stars. For the wormhole inside the black hole, we find an extremal limit where the radius of the throat coincides with the radius of the event horizon and demonstrate that the Hawking temperature vanishes in this limit.

gr-qc↗

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↗

arXiv2023

Spinor domain wall and test fermions on an arbitrary domain wall

We consider a spinor domain wall embedded in a five-dimensional spacetime with a nondiagonal metric. The corresponding plane symmetric solutions for linear and nonlinear spinor fields with different parameters are obtained. It is shown that in the general case the metric functions and spinor fields do not possess $Z_2$ symmetry with respect to the domain wall. We study the angular momentum density of the domain wall arising because of the presence of the spinor field creating the wall. The properties of test fermions located on an arbitrary domain wall are considered. The concepts of the ``second spin'' (arising due to the properties of the Lorentz group generators in a five-dimensional spacetime) and of the ``second magnetic field'' (representing the components $F_{i 5}$ of the electromagnetic field five-tensor) are introduced. We find eigenspinors of the ``second spin'' and show that some of them represent the Bell states. In the nonrelativistic limit we derive the Pauli equation for the test fermions on the domain wall which contains an extra term describing the interaction of a spin-$1/2$ particle with the ``second magnetic field''; this allows the possibility of an experimental verification of the existence of extra dimensions.

gr-qc↗