Gravitation in flat space-time

A previously studied Lorentz-covariant theory of gravitation is given in generally covariant form, i.e., the theory holds for arbitrary reference frames. Flat space-time is a natural condition for the conservation of energy and momentum. The energy-momentum tensor of matter and gravitation is the source of the gravitational field.     

Dissipative fluid in conformally flat space-time

We consider a conformally flat, inhomogeneous solution of the Einstein equations for a dissipative fluid. The production of entropy is found to depend on some arbitrary functions of time. By some subsidiary conditions, such a model is shown to evolve into a homogeneous Friedmann-type universe.     

Ghost neutrino fields in flat space-time

The Weyl neutrino equation is integrated in flat space-time assuming that the energy-momentum tensor of the neutrino field vanishes. It is shown that the flux vector of the neutrino field is tangent to a twist-free and shear-free congruence of null geodesics, which is a special Robinson congruence and constitutes a geometrical representation of a null twistor. It is also shown that, conversely, given such a congruence, a ghost neutrino field can be constructed.     

Another gravitational instability of flat space-time

Witten's demonstration of the instability of the five dimensional Kaluza-Klein ground state can be reduced to four, physical dimensions. One can then conclude that flat space-time at zero temperature with one of the spatial directions wrapped up is unstable. The decay rate is of order exp?L²/16πL²_p where L is the spatial periodicity and L_p is the Planck length. The post tunnelling evolution of the space-time is also discussed.     

Christoffel symbols and inertia in flat space-time theory

A necessary and sufficient criterion of inertia is presented, for the flat space-time theory of general frames of reference, in terms of the vanishing of some typical components of the affine connection pertaining to curvilinear coordinate systems. The physical identification of inertial forces thus arises in the context of the special theory of relativity.     

The general metric for a space-time with a constant vector field

The most general metric that admits a vector field with zero covariant derivative is derived. Some special cases are exhibited.     

Meron and elliptic solutions in conformally flat space-time

The idea recently advanced by the author that particles arise as distortions of a riemannian background is pursued further. Such distortions represent conformally flat solutions of Einstein's “cosmological” equations extremely large “cosmological” constant. It is shown in particular that merons can be generated by perfect fluid or neutral superfluid distributions of energy and momentum. Perfect fluids can also generate elliptic plane waves of the type discussed by Petiau.     

Two theorems on flat space-time gravitational theories

The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-1) function of the 4-velocityu ⁱ , plus a functional of _ij u ⁱ u ^j . The second theorem states that all gravitational theories, that satisfy the strong equivalence principle have a Lagrangian with a first termg _ij (x)u ⁱ u ^j plus an irrelevant term. In both cases the theories must issue from a unique variational principle. Therefore, under this condition it is impossible to find a flat space-time theory that satisfies the strong equivalence principle.     

Long-range scalar field in conformally flat space-time

Consequences of a massless scalar field in conformally flat space-time are studied. Then a wide class of solutions of the scalar field is obtained.     

Electromagnetic field in two-dimensional locally flat space-time

It is shown that an infinite-dimensional symmetry is present in two-dimensional electromagnetic field theory. The generators of the ensuing Virasoro algebra are explicitly calculated both for periodic and antiperiodic fields.     

The parameters of the Lewis metric for the Weyl class

We provide physical interpretation for the four parameters of the stationary Lewis metric restricted to the Weyl class. Matching this spacetime to a completely anisotropic, rigidly rotating, fluid cylinder, we obtain from the junction conditions that one of these parameters is proportional to the vorticity of the source. From the Newtonian approximation a second parameter is found to be proportional to the energy per unit of length. The remaining two parameters may be associated to a gravitational analog of the Aharanov-Bohm effect. We prove, using the Cartan scalars, that the Weyl class metric and static Levi-Civita metric are locally equivalent, i.e., indistinguishable in terms of its curvature.     

Sectional curvature and the determination of the metric in space-time

It is shown that if the sectional (Riemannian) curvature function is given at all spacetime points, then, apart from a very special class of space-times, the metric is uniquely determined.     

First experiment to test whether space-time is flat

From both special and general relativistic gravitational theories, we deduce the predicted value of the precessional angular velocity of a gyroscope caused by the additional gravitational field due to the earth's rotation. The orbiting gyroscope experiment will be the first to test whether space-time is flat.     

Spin-3/2 fields in flat space-time

The equations for the spin-3/2 (Rarita-Schwinger) field given by linearized simple supergravity are written in space-plus-time form in terms ofSU(2) spinors, assuming that the background space-time is flat. Some consequences of these equations are analyzed and a Hamiltonian structure for the Rarita-Schwinger field is obtained.     

Supersymmetric Casimir effect in flat homogeneous Clifford-Klein space-time

The Casimir effect in supersymmetric quantum field theories can occur in spacetime with nontrivial topologies, due to the existence of topologically nonequivalent field configurations. This possibility is considered for the example of the supersymmetric Wess-Zumino model and the N=1 supersymmetric Yang-Mills theory in flat homogeneous Clifford-Klein space-time with the topologies M_n= (S¹)ⁿ×R^4–n, n=1, 2, 3. The occurrence of the Casimir effect in this situation is interesting from the point of view of constructing sensible cosmological scenarios of the early stages of the evolution of the Universe, in particular, the expanding Universe scenario.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 101–106, April, 1987.