An investigation of some of the kinematical aspects of plane symmetric space–times

Abstract

A short review of the literature on plane symmetric space–times (PSSTS) is given in the Introduction. The rest of the paper concerns itself with an investigation of some of the kinematical aspects of PSSTS, i.e., properties of PSSTS which do not depend on the field equations. In particular, the existence of four special coordinate systems is considered. It is shown that the existence of these coordinate systems is not guaranteed for a general Ck (k⩽1) plane symmetric metric (PSM). For k=2, two of the coordinate systems exist in a weak sense whereas the existence of the other two is not guaranteed in any sense. A local intrinsic type classification is introduced in Sec. 3, and it is shown that the existence of an extra Killing vector is correlated to the classification. Finally, the local equivalence of two given PSSTS is considered in Sec. 4. It is shown that some algebraic equations arise from the analysis. These algebraic equations may lead directly to the solution of the problem of the local equivalence of two given PSSTS.