[en] The identification of gravitation with the massless spin 2 gauge field (the gauge group is the group of translations) requires to restrict the solutions of Einstein's equations to the class of topologically trivial manifolds. It is shown that the validity of this restriction in nature is supported by the present-day empirical facts. The identification has a drastic impact on cosmology, because the fulfilment of the cosmological principle seems to be improbable. (author)

[en] The Einstein-Cartan theory of gravitation is an extended version of general relativity assuming the existence of Cartan's contorsion, the antisymmetric part of Christoffel symbols. The theory is intensively studied recently, but the physical meaning of contorsion was not clear earlier. The present paper discusses this question and shows that contorsion is determined in general case by a pair of self-interacting massless spin-2 fields and by other extraordinary vector fields. The spin-2 fields are the gauge fields of Lorentz group. (author)

[en] On the basis of the special relativity and geometrization principle a relativistic gravitation theory (RGT) is unambiguously constructed with the help of a notion of a gravitational field as a physical field in Faraday-Maxwell spirit, which posesses energy momentum and spins 2 and 0. The source of gravitation field is a total conserved energy-momentum tensor for matter and for gravitation field in Minkowski space. In the RGT conservation laws for the energy momentum and angular momentum of matter and gravitational field hold rigorously. The theory explains the whole set of gravitation experiments. Here, due to the geometrization principle the Riemannian space is of a field origin since this space arises effectively as a result of the gravitation field origin since this space arises effectively as a result of the gravitation field action on the matter. The RGT astonishing prediction is that the Universe is not closed but ''flat''. It means that in the Universe there should exist a ''missing'' mass in some form of matter

[en] If a grand Unified Theory with a compact unifying group G is spontaneously broken to H, magnetic monopoles are created. The fate of such an H-monopole under a subsequent breaking to K is contained in H is shown to depend on the behaviour of its non-Abelian charge Q introduced by Goddard, Nuyts, Olive: if Q belongs to the Lie algebra k of K, the monopole survives: if Q can be H-rotated to k, it can be converted. A necessary condition for an H-monopole to survie is that its Higgs charge satisfy a topological constraint

[en] We discuss the possibility that the cosmological constant problem is solved by raising the number of spatial dimensions a la Kaluza-Klein. In (4+2)-dimensional pure gravity theory with the explicit Λ-term we find classical solutions with vanishing physical cosmological constant and compact 2-dimensions. However, there also exist solutions with the non-vanishing physical Λ-term, and the case Λsub(phys)=0 is not preferred at the classical level. We conjecture that quantum corrections and/or additional interactions single out the solution with vanishing physical cosmological constant. (author)

[en] Contrary to the predominant way of doing physics, it is shown that the geometric structure of a general differentiable space-time manifold can be determined by means of the introduction in that manifold of a minimal set of fundamental dynamical quantities associated to a particle endowed with the fundamental property of covariant momentum. Thus, general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and Newtonian dynamics is bound to Newtonian space-time. While in the relativistic instance, the Riemannian character of the manifold is basically fixed by means only of the Hamiltonian state function of the particle (its energy), in the latter case, one have to resort, perhaps not unexpectedly, to the two dynamical entities mass energy, separately. (Author)

[en] Two examples are presented in this paper, the first is unfavorable to the c-boundary construction given by Geroch, Kronheimer and Penrose but in favor of that given by Budic and Sachs, while the second plays an opposite role. The second example is also an example of a causally continuous spacetime with a ''really big gap'', contrary to what was believed in the literature. (author). 10 refs

[en] The chronological order of the events along a space-like path is not invariant under Lorentz transformations, as wellknown. This led to an early conviction that tachyons would give rise to causal anomalies. A relativistic version of the Stuckelberg-Feynman switching procedure (SWP) has been invoked as the suitable tool to eliminate those anomalies. The application of the SWP does eliminate the motions backwards in time, but interchanges the roles of source and dector. This fact triggered the proposal of a host of causal paradoxes. Till now, however, it has not been recognized that such paradoxes can be sensibly discussed (and completely solved, at least in microphysics) only after having properly developed the tachyon relativistic mechanics. We start by showing how to apply the SWP, both in the case of ordiry Special Relativity, and in the case with tachyons. Then, we carefully exploit the kinematics of the tachyon-exchange between to (ordinary) bodies. Being finally able to tackle the tachyon-causality problem, we successively solve the paradoxes: (i) by Tolman-Regge; (ii) by Pirani; (iii) by Edmonds; (iv) by Bell. At last, we discuss a further, new paradox associated with the transmission of signals by modulated tachyon beams

[en] Supergravity has been recoded into superfoliation theory language. For this purpose Csup(4/4N) supertwistor space is determined as space of the fundamental representation of the SN(4/4N) super group. A diagram inducing the tangential foliations diagram has been constructed

[en] A possibility of obtaining the de Sitter and Nariai spacetimes in a generalized theory of gravitation (which was in succession proposed by Utiyama-DeWitt, Parker-Fulling-Hu and Gurovich-Starobinski) is examined. It is shown that the generalized theory with a suitable fixation of three parameters admit both spacetimes, just like the general theory of relativity. (author)