Investigation of self-similar gravitational fields in space-time with plane symmetry

In the framework of general relativity for matter with equation of state p=(γ-1)e gravitational fields with plane symmetry are considered which also admit a conformal group such that the metric depends on z=x1/x0 (self-similar solutions for space-times with plane symmetry). The Einstein equations are thus reduced to a system of ordinary differential equations and its investigation requires a qualitative analysis on two-dimensional phase plane. Some exact solutions are given. The t-region when a coordinate z is timelike and the s-region when z is spacelike are introduced. A special case of structure of the metric which contains plane Friedmann model is considered in detail. Construction of analytic solutions and solutions with weak and strong discontinuities (shock waves and contact discontinuities) is discussed. Solutions are considered which admit conjugation with plane Friedmann model through a weak discontinuity and through a shock wave. A possibility of conjugation of plane Friedmann model and the Minkowski space-time through a shock wave of extreme in-- tensity is discussed