Gravitational wave emission from the numerical evolution of Robinson-Trautman spacetimes: A treatment in the nonlinear regime

The dynamics of a bounded gravitational collapsing configuration emitting gravitational waves is studied. The exterior spacetime is described by Robinson-Trautman geometries and have the Schwarzschild black hole as its final gravitational configuration, when the gravitational wave emission ceases. The nonlinear regime is examined by using the Galerkin method that allows us to reduce the equations governing the dynamics to a finite-dimensional dynamical system, after a proper truncation procedure. Gravitational wave emission patterns from given initial configurations are exhibited for several phases of the collapse and the mass-loss ratio that characterizes the amount of mass extracted by the gravitational wave emission is evaluated. We obtain that the smaller initial mass M-init of the configuration, the more rapidly the Schwarzschild solution is attained and a larger fraction of M-init is lost in the process of gravitational wave emission. Within all our numerical experiments, the distribution of the mass fraction extracted by gravitational wave emission is shown to satisfy the distribution law of nonextensive statistics and this result is independent of the initial configurations considered.