Planary Symmetric Static Worlds with Massless Scalar Sources

الأصل · EN

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]₍₁₁₎, 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 non-spacelike geodesics), are completely free of Cauchy surfaces and contain into the t - leveled sections points which can not be jointed by C¹ - trajectories images of oblique non-spacelike geodesics. Finally, we comment on the possibility of deriving from (M, g±) two other physically interesting ϕ - generated'' spacetimes, by appropiate jonction conditions in the (z = 0) - plane.