Planary Symmetric Static Worlds with Massless Scalar Sources

Details Planary Symmetric Static Worlds with Massless Scalar Sources Planary Symmetric Static Worlds with Massless Scalar Sources

1996-01-26

arxiv.org/abs/gr-qc/9601041v1

Found.Phys. 26 (1996) 1069-1080

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, LaTeX format, figures not included

Scientific paper

10.1007/BF02061404

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 $({\cal M}, {\bf{\rm g}}_{\pm})$ are algebraically special, type $D - [S - 3T]_{(11)}$, and represent globally pathologic spacetimes with a $G_{4}$ - group of motion acting on ${\bf{\rm R}}^{2} \times {\bf{\rm R}}$ orbits. In spite of the model simplicity, these $\phi$ - 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 ${\rm C}^{1}$ - trajectories images of oblique non-spacelike geodesics. Finally, we comment on the possibility of deriving from $({\cal M}, {\bf{\rm g}}_{\pm})$ two other physically interesting ^^ ^^ $\phi$ - generated'' spacetimes, by appropiate jonction conditions in the $(z = 0)$ - plane.

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