On non-linear plane gravitational waves

The nonlinear gravitational waves are exact solutions of Einstein’s equations that describe a radiative field propagating with the speed of light. The non-linearity of Einstein’s equations makes it difficult to track analytical solutions, requiring considerations on the symmetry of the problem. Thus, obtaining radiative solutions, like the pp-waves (plane-fronted gravitational waves with parallel rays), requires considerations about the symmetry and nature of these solutions before the remaining functions are introduced into Einstein’s equations. Obtaining a metric tensor that describes the pp-waves involves advanced mathematical knowledge, making the deductions non-intuitive. The main object of this paper is to obtain the pp-waves metric tensor from simple considerations about the geodesic congruence of theses waves space-time.

Keywords
Non-linear gravitational waves; General Relativity.