Vol 23, No 4 (2017)

A detailed derivation is given of formulas describing the trajectory of a test body moving closely to the ecliptic plane of a rotating star whose gravitational field is modeled by the Kerr metric. It is found that the quasi-elliptic orbit parameters and the revolution period noticeably change (as compared to the classical case), and an additional orbit precession emerges, though four orders of magnitude weaker than that of the Einstein-Schwarzschild case.

We find the probability density distribution of torque orientations in the Universe for the entire period of its evolution. It is shown that in the early Universe the orientation of its spin is random, and the cosmological principle is satisfied. This result is naturally consistent with the CMBisotropy. In the modern Universe the rotation axis direction becomes anisotropic, and the cosmological principle, strictly speaking, is not satisfied. This is confirmed by the large-scale anisotropy in the distribution of space objects and by the torque alignment direction. But since the value of the angular velocity of our Universe is \(\omega_{U_{n}}\sim10^{-19}\;\text{Hz}\), finding of such rotation and its influence on the natural processes is extremely difficult. So today dominates the view that the Universe is isotropic, and the cosmological principle is satisfied in it.

The non-configurational geometrization of the electromagnetic field can be realized using the Model of Embedded Spaces (MES). This model assumes the existence of proper 4D space-time manifolds of particles with a nonzero rest mass and declares that physical space-time is the metric result of the dynamic embedding of these manifolds: the value of the partial contribution of the element manifold is determined by element interactions. The space of the model is provided with a Riemann-like geometry, whose differential formalism is described by a generalization of the gradient operator ∂/∂xⁱ → ∂/∂xⁱ + 2u^k∂²/∂x[ⁱ∂u^k], where uⁱ = dxⁱ/ds is a matter velocity. In the paper, the redshift effect existing in the space of MES is considered, and its electromagnetic component is analyzed. It is shown that for cold matter of the modern Universe this component reduces to a shift in electric fields and is described by the expression \(\Delta {\omega _e}/\omega \simeq \mp \sqrt k \Delta {\varphi _e}/{c^2} = \mp 0.861 \cdot {10^{ - 21}}\Delta {\varphi _e}\left( V \right)\) , where the potential is measured in volts and the sign must be determined experimentally. Testing of the effect is the “experimentum crusis” for MES.

Within the scope of a LRS Bianchi type-I cosmological model we study the role of a nonlinear spinor field in the evolution of the Universe. In doing so, we consider a polynomial type of nonlinearity that describes different stages of the evolution. Finally, we use the observational data to fix the problem parameters that match best with the real picture of the evolution. An assessment of the age of the Universe in the case of a soft beginning of the expansion (initial speed of expansion at the singularity is zero), the age was found to be 15 billion years, whereas in the case of a hard beginning (nonzero initial speed) the Universe is found to be 13.7 billion years old. Values of the constants D₁ and X₁ that define the anisotropy of our model are also calculated.

We consider static, spherically symmetric configurations in general relativity, supported by nonlinear electromagnetic fields with gauge-invariant Lagrangians depending on the single invariant f = F_μνF^μν. After a brief review on black hole (BH) and solitonic solutions, obtained so far with pure electric or magnetic fields, an attempt is made to obtain dyonic solutions, those with both electric and magnetic charges. A general scheme is suggested, leading to solutions in quadratures for an arbitrary Lagrangian function L(f) (up to some monotonicity restrictions); such solutions are expressed in terms of f as a new radial coordinate instead of the usual coordinate r. For the truncated Born-Infeld theory (depending on the invariant f only), a general dyonic solution is obtained in terms of r. A feature of interest in this solution is the existence of a special case with a self-dual electromagnetic field, f ≡ 0 and the Reissner-Nordström metric.

A D-dimensional Einstein–Gauss–Bonnet (EGB) flat cosmological model with a cosmological constant Λ is considered. We focus on solutions with an exponential time dependence of the scale factor. Using the previously developed general stability analysis of such solutions by V.D. Ivashchuk (2016), we apply the criterion from that paper to all known exponential solutions up to the dimension 7 + 1. We show that this criterion, which guarantees the stability of solutions under consideration, is fulfilled for all combinations of the coupling constant of the theory except for some discrete set.

We consider a chiral cosmological model in the framework of Einstein–Gauss–Bonnet cosmology. Using a decomposition of the latter equations in such a way that the first chiral field is responsible for the Einstein part of the model while the second field together with the kinetic interaction is connected with the Gauss–Bonnet part of the theory, we find new exact solutions for the 2-component chiral cosmological model with and without a kinetic interaction between the fields.

We investigate the thermodynamics of the Kerr–Newman–Kasuya black hole and the Reissner–Nordström black hole with a global monopole on inner and outer horizons. Products of surface gravities, surface temperatures, Komar energies, electromagnetic potentials, angular velocities, areas, entropies, horizon radii and irreducible masses at the Cauchy and event horizons are calculated. It is observed that the product of surface gravities, the surface temperature product and the product of Komar energies, electromagnetic potentials and angular velocities at horizons are not universal quantities for these black holes. Products of areas and entropies at the horizons are independent of black hole masses. The heat capacity is calculated for the generalized charged rotating black hole, and a phase transition is observed under certain conditions on r.