Similarity solutions of the Einstein and Einstein-Maxwell equations

E Fischer
1980 Journal of Physics A: Mathematical and General  
Exact solutions of the equations governing vacuum cylindrical gravitational wave spacetimes and colliding plane electromagnetic and plane gravitational wave spacetimes are presented. Both solutions are found by using the geometric technique of Harrison and Estabrook to find appropriate similarity variables to reduce partial differential equations to ordinary differential equations. One of the solutions is transformed into a solution of the Ernst equations.
doi:10.1088/0305-4470/13/4/001 fatcat:zavutbaaxzgnxm7t4ikhsgrb4i