Gravitational interaction for light-like motion in classical and quantum theory

On the basis of an exact vacuum solution of Einstein's equations, {\it vis}. the pencil-of-light field, we study the light-like motion of test and non-test objects. We also consider the quantum theoretical interaction of massless scalar particles through virtual gravitons. The dragging phenomenon is manifested and its agreement with astronomical observations established. This paper submitted to {\bf arXiv} is a somewhat reedited copy of my article dedicated to Dr. Ivar Piir in a volume published on the occasion of his 60th birthday in 1989 in Tartu by the Estonian Academy of Sciences.Comment: LaTeX with babel(English and Russian), 8 pages, no figure

Modelling general relativistic perfect fluids in field theoretic language

Skew-symmetric massless fields, their potentials being $r$-forms, are close analogues of Maxwell's field (though the non-linear cases also should be considered). We observe that only two of them ($r=$2 and 3) automatically yield stress-energy tensors characteristic to normal perfect fluids. It is shown that they naturally describe both non-rotating ($r=2$) and rotating (then a combination of $r=2$ and $r=3$ fields is indispensable) general relativistic perfect fluids possessing every type of equations of state. Meanwile, a free $r=3$ field is completely equivalent to appearance of the cosmological term in Einstein's equations. Sound waves represent perturbations propagating on the background of the $r=2$ field. Some exotic properties of these two fields are outlined.Comment: 23 pages, 0 figures (LaTeX

On a new category of physical effects

A new category of "intrinsic" effects is proposed to be added to the two already known kinematic and dynamical categories. An example of intrinsic effect is predicted, its origin source is established, and a scheme of its experimental detection is proposed. This effect lowers to non-relativistic values the propagation velocity of a plane electromagnetic wave in a vacuum, when a time-independent homogeneous magnetic field is superposed over it. This result, pertaining to the classical Maxwell theory, follows from exact calculations. A critical remark on gravitational waves' detection is given.Comment: 4 pages, 1 figure, RevTeX 4.1; one PACS number is correcred, a new reference added, and the role of geodesic deviation equation is clarified

Lienard-Wiechert solution revisited

A self-consistent consideration of the Lienard-Wiechert solition is given including its heuristic deduction, which involves a future light cone (thus the lightlike propagation of information from an arbitrarily moving pointlike charge), and physical interpretation of this field via application of three distinct reference frames (of an inertial observer, then a non-inertial one retardedly co-moving with the charged source, and finally, co-moving with the electromagnetic field). In the last frame the magnetic part of the Lienard-Wiechert field identically (though not asymptotically) vanishes in all spacetime together with the Poynting vector. In the second frame, the properties of energy redistribution and radiation of the field are discussed. The dynamically caused propagation velocity of the Lienard-Wiechert electromagnetic field in a vacuum at any final distance from the source is less than that of light.Comment: 24 pages, no figures, Late

Relativistic generalization of the inertial and gravitational masses equivalence principle

The Newtonian approximation for the gravitational field equation should not necessarily involve admission of non-relativistic properties of the source terms in Einstein's equations: it is sufficient to merely consider the weak-field condition for gravitational field. When a source has electromagnetic nature, one simply {\em cannot} ignore its intrinsically relativistic properties, since there cannot be invented any non-relativistic approximation which would describe electromagnetic stress-energy tensor adequately, even at large distances where the fields become naturally weak. But the test particle on which gravitational field is acting, should be treated as non-relativistic (this premise is required for introduction of the Newtonian potential $\Phi_{\rm N}$ from the geodesic equation).Comment: 5 pages, a talk delivered at the 11th Marcel Grossmann Meeting (Session GT4), Berlin, 200

Discrete model of spacetime in terms of inverse spectra of the T0T_0 Alexandroff topological spaces

The theory of inverse spectra of $T_0$ Alexandroff topological spaces is used to construct a model of $T_0$-discrete four-dimensional spacetime. The universe evolution is interpreted in terms of a sequence of topology changes in the set of $T_0$-discrete spaces realized as nerves of the canonical partitions of three-dimensional compact manifolds. The cosmological time arrow arises being connected with the refinement of the canonical partitions, and it is defined by the action of homomorphisms in the proper inverse spectrum of three-dimensional $T_0$-discrete spaces. A new causal order relation in this spectrum is postulated having the basic properties of the causal order in the pseudo-Riemannian spacetime however also bearing certain quasi-quantum features. An attempt is made to describe topological changes between compact manifolds in terms of bifurcations of proper inverse spectra; this led us to the concept of bispectrum. As a generalization of this concept, inverse multispectra and superspectrum are introduced. The last one enables us to introduce the discrete superspace, a discrete counterpart of the Wheeler--DeWitt superspace.Comment: LaTeX, 39 pages, no figure

Anti-de Sitter-type 2+1 spacetime of a charged rotating mass

The exact charged rotating solution of 2+1 Einstein-Maxwell equations with $\Lambda$ term is obtained and its properties outlined. It generalizes the Cataldo-Cruz-del Campo-Garc{\'\i}a relativistic charged massive black hole on the 2+1 anti-de Sitter cosmological background. We show that rotating solutions correspond to inhomogeneous field equations, thus presence of sources in 2+1 Maxwell's equations cannot be identified with existence of a charge distribution. Instead, these sources are related to the 2+1 Machian 2-form field, and the overall Lagrangian structure of the rotating system is reconstructed.Comment: 9 pages, LaTeX file using amssym.def; corrected references and extended conten

Classification of electromagnetic fields in general relativity and its physical applications

The simplest electromagnetic fields' (general- as well as special-relativistic) classification is formulated which is based on physically motivated ideas. According to this classification these fields can belong to three types (electric, magnetic and null), each of them being split in pure and impure subtypes. Only pure null type field propagates with the fundamental velocity $c$, all other fields have the propagation velocity less than that of light. The reference-frame-based methods of elimination of alternative three-fields (e.g., magnetic in the electric type case) are given for pure subtypes; for pure null type the generalized Doppler effect takes place instead. All three types of impure fields are shown to be {\bf E}-{\bf B}-parallelizable. Thus such an elimination in pure non-null and parallelization in all impure cases mean transformation to the reference frame co-moving with the electromagnetic field in which the Poynting vector vanishes. The methods we propose modernizing the Rainich--Misner--Wheeler approach, also permit to construct new exact Einstein--Maxwell solutions from already known seed solutions. As examples, the Kerr--Newman and Li\'enard--Wiechert solutions are considered, three ``new'' types of rotating charged black holes (with the same Kerr-Newman geometry) are presented, and new physical effects are evaluated. PACS 2008 Numbers: 04.20-{\bf q}, 04.20.Ex, 04.40.Nr, 04.70.BwComment: 28 pages, no figure

Relativistic Physics in Arbitrary Reference Frames

In this paper we give a review of the most general approach to description of reference frames, the monad formalism. This approach is explicitly general covariant at each step, permitting to use abstract representation of tensor quantities; it is applicable also to special relativity when non-inertial effects are considered in its context; moreover, it involves no hypotheses whatsoever thus being a completely natural one. For the sake of the reader's convenience, a synopsis of tensor calculus in pseudo-Riemannian space-time precedes discussion of the subject, containing expressions rarely encountered in literature but essentially facilitating the consideration. We give also a comparison of the monad formalism with the other approaches to description of reference frames in general relativity. In three chapters we consider applications of the monad formalism to general relativistic mechanics, electromagnetic and gravitational fields theory. Alongside of the general theory, which includes the monad representation of basic equations of motion of (charged) particles and of fields, several concrete solutions are provided to clarify the physical role and practical application of reference frames (e.g., cases when a rotating electrically charged fluid does not produce any electric field in its co-moving reference frame, or kinematic magnetic charges arise in a rotating frame). The cases are discussed when it is unnecessary to introduce a reference frame, and when such an introduction is essential. Special attention is dedicated to analogy between gravitation, electromagnetism and mechanics (e.g., the dragging phenomenon and existence in the Maxwell equations in rotating frames of terms of the same nature as that of the Coriolis and centrifugal forces).Comment: 137 pages, LaTeX type, amssym.def, amssy

A T0T_0-discrete universe model with five low-energy fundamental interactions and the coupling constants hierarchy

A quantum model of universe is constructed in which values of dimensionless coupling constants of the fundamental interactions (including the cosmological constant) are determined via certain topological invariants of manifolds forming finite ensembles of 3D Seifert fibrations. The characteristic values of the coupling constants are explicitly calculated as the set of rational numbers (up to the factor $2\pi$) on the basis of a hypothesis that these values are proportional to the mean relative fluctuations of discrete volumes of manifolds in these ensembles. The discrete volumes are calculated using the standard Alexandroff procedure of constructing $T_0$-discrete spaces realized as nerves corresponding to characteristic canonical triangulations which are compatible with the Milnor representation of Seifert fibered homology spheres being the building material of all used 3D manifolds. Moreover, the determination of all involved homology spheres is based on the first nine prime numbers ($p_1=2, >..., p_9=23$). The obtained hierarchy of coupling constants at the present evolution stage of universe well reproduces the actual hierarchy of the experimentally observed dimensionless low-energy coupling constants.Comment: RevTeX4 6 page