MG11 
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Topological gravity on graph manifolds

We propose a cosmological model of the BF-type (topological gravitation) in which the coupling constants are identified with the basic topological invariants of four-dimensional manifolds, namely the intersection matrices of graph manifolds describing Euclidean spacetime regions. A succession of graph manifolds is constructed representing topology transitions related to changes of number of fundamental pre-interactions as well as of their hierarchy. In this model the topological description of universe involves a superposition of different topologies of spatial sections resulting from splicing of the elementary three-dimensional Seifert fibred homology spheres being spliced in accordance with the graphs under consideration. The averaged intersection matrix obtained for the proposed ensemble of graph manifolds describes the hierarchy of low-energy coupling constants of fundamental interactions observed in the real universe. Our extended Abelian BF-model bears naive marks of the low-energy effective $U(1)^r$ Seiberg--Witten theory. In our model, the coupling constants matrices are the spacetime topological invariants, while in the Seiberg--Witten theory coupling constants matrices are topological invariants (period matrices) of the space of vacuum solutions modulo gauge transformations (the moduli space).

Relativistic generalization of the inertial and gravitational masses equivalence principle

Usually the equivalence principle is established from Einstein's theory with assumptions of both non-relativistic and weak field approximations. However some gravitating systems do not admit non-relativistic approximation, e.g. electromagnetic fields' stress-energy tensor always has zero trace. Thus, dismissing the non-relativistic character of the source and retaining it only for bodies moving in the source's field, we come from Einstein's equations to different relations between inertial and gravitating masses of sources (doubling and quadrupling the gravitational mass for electromagnetic source and stiff matter, respectively). Some physical consequences are discussed.

Electromagnetism and perfect fluids interplay in multidimensional spacetimes

It is shown that in the physical interpretation of different fields (in the sense of their tensor rank etc.) crucially depends on the number of spacetime dimensions $D$ under consideration. In particular, the vector massless field is justly interpreted as electromagnetic in $D=4$ (3+1), but in $D=3$ (2+1) it has the energy-momentum tensor identical with that of a perfect fluid. It is demonstrated that the true analogues of electromagnetic field exist only in even-dimensional spacetimes.

Nariai--Bertotti--Robinson spacetimes as a building material for one-way wormholes with horizons, but without singularity

Generalizations of the Nariai spacetime involving also electromagnetic field (of the Bertotti--Robinson type) without singularities are considered. It is shown that they possess horizons and can be glued to spacetimes of Reissner--Nordstroem with cosmological constant from both sides, thus forming a one-way wormhole connecting these spacetimes, with finite duration of the journey through the wormhole (in traveller's proper time).

Zeeman-type dragging in the Kerr--Newman and NUT spacetimes

In Boyer--Lindquist coordinates in the Kerr--Newman spacetime, a test neutral particle in a circular orbit in the equatorial plane outside the ergosphere executes a motion with the period differing from that executed around a purely Kerr centre by the presence of the charge term only. Thus the meeting point of two particles moving along the same orbit in opposite directions is rotating counter the rotation of the Kerr--Newman centre. In the Taub--NUT spacetime, the motion of a test particle occurs in similar situation in the plane moved away from the ``equatorial plane'' by the distance determined by the central mass, NUT parameter $k$ and the orbit radius, in directions upwards or downwards, depending on relative signs of $k$ and the angular momentum of the particle.