Том 24, № 2 (2018)

Distortion of classical elliptical orbits of the Apollo asteroids (crossing the Earth’s orbit) in the gravitational field modeled by the Kerr metric, is calculated, and a numerical assessment is given to the general-relativistic impact on the near-Earth motion of potentially hazardous objects (PHO).

We are concerned with the precise modalities by which mathematical constructions related to energy tensors can be adapted to a tetrad-affine setting. We show that, for fairly general gauge field theories formulated in that setting, two notions of energy tensor (the canonical tensor and the stress-energy tensor) exactly coincide with no need for tweaking. Moreover, we show how both notions of energy tensor can be naturally extended to include the gravitational field itself, represented by a couple constituted by the tetrad and the spinor connection. Then we examine the on-shell divergences of these tensors in relation to the issue of local energy conservation in the presence of torsion.

The geometric and relational approach to the unified description of gravity and electromagnetism are considered. In the framework of the relational theory, as well as multidimensional geometric models of Kaluza–Klein type, some arguments are invoked in support of Einstein’s hypothesis on a small charge asymmetry of elementary particles and Sutherland’s hypothesis on the origin of the magnetic fields of the Earth, the Sun and other astrophysical objects. According to this hypothesis, effective currents created by bulk and surface charges contribute to the dynamics of the magnetic field of planets. Estimates of this effect for various astrophysical objects are made.

Within the scope of multidimensional Kaluza–Klein gravity with nonlinear curvature terms and two spherical extra spaces of dimensions m and n, we study the properties of an effective action for the scale factors of extra dimensions. Dimensional reduction leads to an effective 4D multiscalar-tensor theory. Based on qualitative estimates of the Casimir energy contribution at a physically reasonable length scale, we demonstrate the existence of such sets of the initial parameters of the theory in the case m = n that provide a minimum of the effective potential at this scale which yields a fine-tuned value of the effective 4D cosmological constant The corresponding size of extra dimensions depends of which conformal frame is interpreted as the observational one: it is about three orders of magnitude larger than the standard Planck length if we adhere to the Einstein frame, but it is n-dependent in the Jordan frame, and its invisibility requirement restricts the total dimension to values D = 4 + 2n ≤ 20.

An exact determination of the Hubble constant remains one of key problems in cosmology for almost a century. However, its modern values derived by various methods still disagree from each other by almost 10%, larger values being obtained by measurements at relatively small distances (e.g., by Cepheid stars as standard candles), while smaller values are characteristic of the methods associated with huge spatial scales (e.g., from the analysis of cosmic microwave background fluctuations). A reasonable way to resolve this puzzle is to assume that the Hubble constant is inherently scale-dependent. This idea seems to be particularly attractive in the light of the latest observational results on the early-type galaxies, where dark matter halos are almost absent. Therefore, an average contribution of the irregularly distributed dark matter to the rate of the cosmological expansion should be substantially different at various spatial scales. As follows from rough estimates, the corresponding variation of the Hubble constant can be about 10% and even more, which well explains the spread in its values obtained by different methods.

The algebraic classification of stress-energy tensors includes tensors whose symmetry is partly broken as compared with Einstein’s maximally symmetric cosmological term. This allows us to introduce, in a general setting, a vacuum dark fluid with variable density and pressures approaching the cosmological constant in certain space-time regions. The relevant class of Einstein equations describes cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy and compact objects with de Sitter interiors generically related to vacuum dark energy, which can be responsible for observational effects typical of dark matter. The mass of objects is generically related to breaking of space-time symmetry from the de Sitter group. We outline the basic generic properties of regular cosmological models with vacuum dark energy, and of dark matter candidates with de Sitter interiors, including their observational signatures.

Spatially homogeneous and anisotropic Bianchi type-I cosmological models of Brans–Dicke (BD) theory of gravitation are investigated. The model represents an accelerating universe at present and is considered to be dominated by dark energy. The cosmological constant Λ is considered as a candidate for dark energy. The derived model agrees at par with the recent SN Ia observations. We have set the BD coupling constant ω to be 40000, according to the solar system tests and evidence. We discuss various physical and geometric properties of the models and compare them with the corresponding general-relativistic models.