The classification of static plane-symmetric spacetimes

Taub (in General Relativity. edited by L. O' Raifeartaigh (Clarenlon Press) 1972, p. 133) discussed the plane-symmetric similarity solutions for selfgravitating fluids. Hall and Steelc (Grn. Rclat Gravit , 22 (1990) 457) investigated space-times admitting a proper homothety vector field upto their Segre and Petrov tvpos. Here a complete classification of static plane-symmetric spacetimes according to their isometrie;-. (homotheties) and metrics is provided, without imposing any restriction on the stress-energy tensor. It turns out that these sapacetimes admit G_r (r =4. 5.6. 7, 10) as the maximal isometry groups whereas their homothety groups are H_m (m = 5. 7 11). In each case the metric along with their Killing (homothety) vector fields are obtained. The Einstein Held equations are then used to discuss the stress energy tensors of the spHcrtimes admitting higher symmetries along with their Segre and Plebanski types and finally results are compared with those of Taub. Hall and Stoele.