Electromagnetism and perfect fluids interplay in multidimensional spacetimes

We consider fields in (D>2)-dimensional spacetime, whose potential is r-form (skew-symmetric tensor of rank r), the field tensor F being its exterior derivative and the Lagrangian, a function of the quadratic invariant I of this tensor. It is shown that vector field (r=1) describes electromagnetic field only for D=4. In particular, for D=3 and the Lagrangean L as any function of the above-mentioned invariant, the (r=1)-field has energy-momentum tensor identical with that of a perfect fluid whose equation of state depends on the choice of L(I).Comment: 5 pages, a talk delivered at the 11th Marcel Grossmann Meeting (2006

Geometric phase shift for detection of gravitational radiation

An effect of geometrical phase shift is predicted for a light beam propagating in the field of a gravitational wave. Gravitational radiation detection experiments are proposed using this new effect, the corresponding estimates being given.Comment: LaTeX2e, 12 p

Topological gravitation on graph manifolds

A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the topological structure of our universe.Comment: 3 pages, a talk delivered at the 11th Marcel Grossmann Meeting (2006

Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity

A new quasigroup approach to conservation laws in general relativity is applied to study asymptotically flat at future null infinity spacetime. The infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to the Poincar\'e quasigroup and the Noether charge associated with any element of the Poincar\'e quasialgebra is defined. The integral conserved quantities of energy-momentum and angular momentum are linear on generators of Poincar\'e quasigroup, free of the supertranslation ambiguity, posess the flux and identically equal to zero in Minkowski spacetime.Comment: RevTeX4, 5 page

Gravitomagnetism and Relative Observer Clock Effects

The gravitomagnetic clock effect and the Sagnac effect for circularly rotating orbits in stationary axisymmetric spacetimes are studied from a relative observer point of view, clarifying their relationships and the roles played by special observer families. In particular Semer\'ak's recent characterization of extremely accelerated observers in terms of the two-clock clock effect is shown to be complemented by a similarly special property of the single-clock clock effect.Comment: 19 pages, LaTeX, IOP macros with package epsf and 1 eps figure, to appear in Classical and Quantum Gravity, slight revisio

Topological gravity on plumbed V-cobordisms

An ensemble of cosmological models based on generalized BF-theory is constructed where the role of vacuum (zero-level) coupling constants is played by topologically invariant rational intersection forms (cosmological-constant matrices) of 4-dimensional plumbed V-cobordisms which are interpreted as Euclidean spacetime regions. For these regions describing topology changes, the rational and integer intersection matrices are calculated. A relation is found between the hierarchy of certain elements of these matrices and the hierarchy of coupling constants of the universal (low-energy) interactions. PACS numbers: 0420G, 0240, 0460Comment: 29 page

Gravitational Couplings of Intrinsic Spin

The gravitational couplings of intrinsic spin are briefly reviewed. A consequence of the Dirac equation in the exterior gravitational field of a rotating mass is considered in detail, namely, the difference in the energy of a spin-1/2 particle polarized vertically up and down near the surface of a rotating body is $\hbar\Omega\sin\theta$. Here $\theta$ is the latitude and $\Omega = 2GJ/(c^2 R^3)$, where $J$ and $R$ are, respectively, the angular momentum and radius of the body. It seems that this relativistic quantum gravitational effect could be measurable in the foreseeable future.Comment: LaTeX file, no figures, 16 page

Quantum Theory in Accelerated Frames of Reference

The observational basis of quantum theory in accelerated systems is studied. The extension of Lorentz invariance to accelerated systems via the hypothesis of locality is discussed and the limitations of this hypothesis are pointed out. The nonlocal theory of accelerated observers is briefly described. Moreover, the main observational aspects of Dirac's equation in noninertial frames of reference are presented. The Galilean invariance of nonrelativistic quantum mechanics and the mass superselection rule are examined in the light of the invariance of physical laws under inhomogeneous Lorentz transformations.Comment: 25 pages, no figures, contribution to Springer Lecture Notes in Physics (Proc. SR 2005, Potsdam, Germany, February 13 - 18, 2005