Plane Symmetric Static Spacetimes Research Articles

On the sources of static plane symmetric vacuum space-times

The sources of static vacuum plane space-times with reflection symmetry are considered. It is argued that the counterpart of the Einstein theory to the gravitational field of a massive Newtonian plane should be described by the Rindler solution, which represents also a uniform gravitational field, and the test particles moving in which have constant accelerations.

The classification of static plane symmetric space–times according to their Ricci collineations

Static plane symmetric space–times are classified according to their Ricci collineations (RCs). Their relation with isometries of the space–times is established. Unlike the spherically symmetric space–times, some metrics are found for a nondegenerate Ricci tensor which have more RCs than isometries.

The regularity of static spherically cylindrically and plane symmetric spacetimes at the origin

We find the necessary and sufficient conditions for the regularity of all scalar invariants polynomial in the Riemann tensor at the origin of spherically, cylindrically and plane symmetric static spacetimes under the assumption that the metric functions are sufficiently smooth there. These conditions turn out to be simple enough to allow a check for regularity by inspection.

Static plane-symmetric space-time with a conformally coupled massless scalar field

We investigate static plane-symmetric space-times. The source of curvature in the Taub space is identified, and the modification hereof due to the presence of a conformally coupled scalar field is calculated. For a specific value of the scalar charge, the scalar field has an energy-momentum tensor of the Casimir type. In this case the source is a domain wall.

C-boundary of Taub's plane-symmetric static vacuum spacetime.

To describe singularities using the notion of c-boundary, it is necessary to divide the c-boundary into two portions, one of them represents the singularity while the other represents infinity. By investigating the global structure of Taub's plane-symmetric static spacetime in detail we prove that the singular portion of the c-boundary of this spacetime is a single point. This suggests that it might not be fruitful describing the structure of singularities using the c-boundary construction. The possible difficulty in singling out the ``singular portion'' of the c-boundary is also discussed.

Static space-time in general scalar tensor theory

The problem of the coupled Einstein–Maxwell scalar field in the framework of general scalar tensor theory of Nordtvedt is completely solved for plane symmetric static matter-free space-time. Special cases are considered for some special choices of ω as functions of the scalar field. Solutions are gien also in the absence of the electromagnetic field and these are shown to generate a few special cases of Bianchi I cosmological models when subject to a set of complex transformations of coordinates.