Alexander B. Balakin

Curvature force and dark energy

A curvature self-interaction of the cosmic gas is shown to mimic a cosmological constant or other forms of dark energy, such as a rolling tachyon condensate or a Chaplygin gas. Any given Hubble rate and deceleration parameter can be traced back to the action of an effective curvature force on the gas particles. This force self-consistently reacts back on the cosmological dynamics. The links between an imperfect fluid description, a kinetic description with effective antifriction forces and curvature forces, which represent a non-minimal coupling of gravity to matter, are established.

Non-minimal coupling for the gravitational and electromagnetic fields: A General system of equations

We establish a new self-consistent system of equations for the gravitational and electromagnetic fields. The procedure is based on a non-minimal nonlinear extension of the standard Einstein–Hilbert–Maxwell action. General properties of a three-parameter family of non-minimal linear models are discussed. In addition, we show explicitly that a static spherically symmetric charged object can be described by a non-minimal model, second order in the derivatives of the metric, when the susceptibility tensor is proportional to the double-dual Riemann tensor.

Non-minimal coupling of photons and axions

We establish a new self-consistent system of equations accounting for a non-minimal interaction of gravitational, electromagnetic and axion fields. The procedure is based on a non-minimal extension of the standard Einstein-Maxwell-axion action. The general properties of a ten-parameter family of non-minimal linear models are discussed. We apply this theory to the models with pp-wave symmetry and consider propagation of electromagnetic waves non-minimally coupled to the gravitational and axion fields. We focus on exact solutions of electrodynamic equations, which describe quasi-minimal and non-minimal optical activity induced by the axion field. We also discuss empirical constraints on coupling parameters from astrophysical birefringence and polarization rotation observations.

Nonminimal coupling for the gravitational and electromagnetic fields: Traversable electric wormholes

We discuss new exact solutions of a three-parameter nonminimal Einstein-Maxwell model. The solutions describe static spherically symmetric objects with and without center, supported by an electric field nonminimally coupled to gravity. We focus on a unique one-parameter model, which admits an exact solution for a traversable electrically charged wormhole connecting two universes, one asymptotically flat the other asymptotically de Sitter ones. The relation between the asymptotic mass and charge of the wormhole and its throat radius is analyzed. The wormhole solution found is thus a nonminimal realization of Wheelers idea about charge without charge and shows that, if the world is somehow nonminimal in the coupling of gravity to electromagnetism, then wormhole appearance, or perhaps construction, is possible.

Non-minimal Wu–Yang monopole

Abstract We discuss new exact spherically symmetric static solutions to non-minimally extended Einstein–Yang–Mills equations. The obtained solution to the Yang–Mills subsystem is interpreted as a non-minimal Wu–Yang monopole solution. We focus on the analysis of two classes of the exact solutions to the gravitational field equations. Solutions of the first class belong to the Reissner–Nordstrom type, i.e., they are characterized by horizons and by the singularity at the point of origin. The solutions of the second class are regular ones. The horizons and singularities of a new type, the non-minimal ones, are indicated.

Regular nonminimal magnetic black holes in spacetimes with a cosmological constant

We consider new regular exact spherically symmetric solutions of a nonminimal Einstein--Yang-Mills theory with a cosmological constant and a gauge field of magnetic Wu-Yang type. The most interesting solutions found are black holes with metric and curvature invariants that are regular everywhere, i.e., regular black holes. We set up a classification of the solutions according to the number and type of horizons. The structure of these regular black holes is characterized by four specific features: a small cavity in the neighborhood of the center, a repulsion barrier off the small cavity, a distant equilibrium point, in which the metric function has a minimum, and a region of Newtonian attraction. Depending on the sign and value of the cosmological constant the solutions are asymptotically de Sitter (dS), asymptotically flat, or asymptotically anti-de Sitter (AdS).

Nonminimal Wu-Yang wormhole

We discuss exact solutions of a three-parameter nonminimal Einstein-Yang-Mills model, which describe the wormholes of a new type. These wormholes are considered to be supported by the SU(2)-symmetric Yang-Mills field, nonminimally coupled to gravity, the Wu-Yang ansatz for the gauge field being used. We distinguish between regular solutions, describing traversable nonminimal Wu-Yang wormholes, and black wormholes possessing one or two event horizons. The relation between the asymptotic mass of the regular traversable Wu-Yang wormhole and its throat radius is analyzed.

Gradient models of the axion-photon coupling

We establish an extended version of the Einstein–Maxwell-axion model by introducing into the Lagrangian cross-terms, which contain the gradient four-vector of the pseudoscalar (axion) field in convolution with the Maxwell tensor. The gradient model of the axion–photon coupling is applied to cosmology: we analyze the Bianchi-I type Universe with an initial magnetic field, electric field induced by the axion–photon interaction, cosmological constant and dark matter, which is described in terms of the pseudoscalar (axion) field. Analytical, qualitative and numerical results are presented in detail for two distinguished epochs: first, for the early Universe with magnetic field domination; second, for the stage of late-time accelerated expansion.

Optical metrics and birefringence of anisotropic media

The material tensor of linear response in electrodynamics is constructed out of products of two symmetric second rank tensor fields which in the approximation of geometrical optics and for uniaxial symmetry reduce to “optical” metrics, describing the phenomenon of birefringence. This representation is interpreted in the context of an underlying internal geometrical structure according to which the symmetric tensor fields are vectorial elements of an associated two-dimensional space.

Singular behaviour of electric and magnetic fields in dielectric media in a nonlinear gravitational wave background

Evolution of electric and magnetic fields in dielectric media, driven by the influence of a strong gravitational wave, is considered for four exactly integrable models. It is shown that the gravitational wave field gives rise to new effects and to singular behaviour in the electromagnetic field.