GRAVITATIONAL WAVE EMISSION FROM A BOUNDED
SOURCE:
A TREATMENT IN THE FULL NONLINEAR REGIME
I. Damião Soares
(Centro Brasileiro de Pesquisas Fisicas/MCT-Rio de Janeiro)
H.P. Oliveira (Instituto
de Física-Universidade do Estado do Rio de Janeiro)
O.C. Castellani
(Centro Brasileiro de Pesquisas Fisicas/MCT-Rio de Janeiro)
We study the dynamics of a
bounded collapsing configuration emitting gravitational waves, by using
Robinson-Trautman spacetimes, having the Schwarzschild black-hole as its final
gravitational configuration. The full nonlinear regime is examined by using the
Galerkin projection method through which the partial differential equations
governing the dynamics is transformed into a dynamical system after a proper
truncation procedure. The invariant characterization of the gravitational
wave-zone and the amplitudes of the gravitational wave emission is made through
the analysis of the structure of the curvature tensor and the use of the
Peeling Theorem. Gravitational wave emission patterns from given initial
configurations of the source are exhibited for several phases of the collapse.
We also examine the decreasing of the associated Bondi mass function that
characterizes the amount of mass extacted by the gravitational waves emitted.