25 research outputs found
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 -forms, are close
analogues of Maxwell's field (though the non-linear cases also should be
considered). We observe that only two of them (2 and 3) automatically yield
stress-energy tensors characteristic to normal perfect fluids. It is shown that
they naturally describe both non-rotating () and rotating (then a
combination of and fields is indispensable) general relativistic
perfect fluids possessing every type of equations of state. Meanwile, a free
field is completely equivalent to appearance of the cosmological term in
Einstein's equations. Sound waves represent perturbations propagating on the
background of the 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
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 Alexandroff topological spaces
The theory of inverse spectra of Alexandroff topological spaces is used
to construct a model of -discrete four-dimensional spacetime. The universe
evolution is interpreted in terms of a sequence of topology changes in the set
of -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
-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
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 , 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
Anti-de Sitter-type 2+1 spacetime of a charged rotating mass
The exact charged rotating solution of 2+1 Einstein-Maxwell equations with
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
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 -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 ) 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 -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 (). 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