Evolution of plane-symmetric self-similar space-times containing perfect fluid

Space-times with plane symmetry are considered which also admit a conformal group such that the metric depends on the variablez=x¹/x⁰ (homothetic or self-similar solutions). Different regions depending on the space-time character ofz can be discerned in each solution: thet region whenz is timelike and thes-region whenz is spacelike. Exact solutions of the Einstein equations are given for an energy-momentum tensor corresponding to an ideal fluid with equation of statep=(-1)e. Different types of solutions occur depending upon the value of in the equation of state, and these are studied using phase-plane methods. The solutions of considered type in the Minkowski space-time are also given.