Motivated by the recent wave of investigations on plane domain wall spacetimes with nontrivial topologies, the present paper deals with (probably) the most simple source field configuration which can generate a spatially planary symmetric static spacetime, namely a minimally coupled massless scalar field that depends only upon a spacelike coordinate. z. It is shown that the corresponding exact solutions (ℳ. g±) are algebraically special, type D-[S-3T] (in11), and represent globally pathologic spacetimes with a G4-group of motion acting on R2 × (...) R orbits. In spite of the model simplicity, these Φ-generated worlds possess naked timelike singularities (reached within a finite universal time by normal nonspacelike geodesics). are completely free of Cauchy surfaces, and contain, in the t-leveled sections, points that cannot be joined by C1-trajectory images of oblique non-spacelike geodesies. Finally, we comment on the possibility of deriving from (ℳ, g±) two other physically interesting Φ-generated” spacetimes by appropriate joining conditions in the (z=0)-plane. (shrink)

The \\)-Robertson–Walker spacetime is under investigation. With the derived Hamilton operator, we are solving the Wheeler–De Witt Equation and its Schrödinger-like extension, for physically important forms of the effective potential. The closed form solutions, expressed in terms of Heun’s functions, allow us to comment on the occurrence of Universe from highly probable quantum states.

The tetradic Lorentz-gauge invariant formulation of the SU(2) × U(1) theory in S3 × R space-time is presented and the general gauge covariant Dirac-Klein-Gordon-Maxwell-Yang-Mills equations are derived. A direct comparison of these equations to those of the SU(2) × U(1) gauge theory on Minkowskian background points out major differences effectively induced by the minimally coupling to S3 × R gravity.