Evolution of angular momentum and multipole structure of perturbed Robinson-Trautman spacetimes

OSVALDO M. MORESCHI; LUIS LEHNER

Ngonyama, Krugerdorp, Sud África

Workshop; nr2001, International Workshop on Numerical Relativity; 2001

Perturbations of Robinson-Trautman spacetimes have been used for estimating the gravitational radiation in the non-head-on black hole collision. The physical situation was model with the prescription that the shear should be zero. The equations that govern the structure of an asymptotically flat spacetime at future null infinity, can be arranged in such a way that some fields are given on a initial section of scri, and prescribing the free radiation data, one can evolve all the physical fields in terms of the retarded time. In order to describe an isolated system within a given accuracy, one might think that it is only necessary to consider a particular multipolar expansion of the fields up to certain degree. Many years ago, Janis and Newman(1965) pointed out that in linearized gravity the prescription of a particular finite multipolar expansion impose conditions of the radiation data; described for example by the Bondi shear. Here we study different prescriptions for setting the free data at future null infinity and study the evolution of angular momentum and multipole structure for several cases. This numerical treatment serves in particular to set up a code that we intend to use for general asymptotically flat spacetimes. In the present work we are interested in the mathematical behavior of the structure asymptotic equations. In future work we intend to apply this equations to physical realistic situations.