Matching of the plane symmetric static and homogeneous vacuum solutions of the Einstein field equations

Abstract

The Taub plane symmetric static and homogeneous vacuum solutions are matched on a natural hypersurface. The space–times obtained in this way have distribution valued curvature tensors along the joining hypersurfaces. Our treatment of this problem follows Taub’s presentation of space–times with distribution valued curvature tensors. We find that the surfaces of the join may be interpreted as thin null pressureless fluid shocks. The nature of these surfaces are further investigated by examining the behavior of geodesics crossing the surfaces.