Plane symmetric perfect fluid distributions admitting a one-parameter- group of conformal motion

Abstract

Some exact analytic solutions of Einstein's equations with perfect fluid source have been found, under the assumptions of (i) plane symmetry and (ii) the existence of a one- parameter group of conformal motions, with the generator in the hypersurface. The solutions are algebraically special (Petrov type D) and belong to class I of Wainwright classifications. They are non- static with non- vanishing shear. First of the solutions represent an expanding homogeneous distribution of matter, which evolves from a singular state at t=O. Second one is conformally fiat and represents homogeneous density, but inhomogeneous pressure distributions with shear - free motions. The last solution is inhomogeneous in density as well as pressure