Statistics – Applications
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008mgm..conf.1633v&link_type=abstract
"THE ELEVENTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation an
Statistics
Applications
Scientific paper
The most powerful source of gravitational radiation is the merger of a black hole with another black hole (or other compact object such as a neutron star). Such processes need to be calculated numerically, and the field of numerical relativity has been developed to tackle such problems. The most popular approach to numerical relativity is based on the ADM formalism, and variations thereof. We however take the alternative approach to numerical relativity based on an evolution of the metric variables in the Bondi-Sachs form. To date, applications involving black holes have been restricted to the Schwarzschild case, because of the lack of initial and boundary data for a rotating black hole. We obtained a Kerr metric in Bondi-Sachs form which can provide such initial data. Our point of departure, was the Kerr geometry as obtained by Pretorius and Israel.3 We made coordinate transformations on this metric, to bring it into Bondi-Sachs form. We confirmed elementary flatness of this metric, and we also confirmed that it is asymptotic to the Bondi-Sachs form of the Schwarzschild geometry. The results obtained in our paper1 are needed so that numerical relativity codes based on the characteristic formalism, can be applied to a situation that contains a rotating black hole. In order to validate the metric, we evaluate it numerically on a regular grid of the new coordinates. The Ricci tensor is then computed, for different discretizations, and was found to be convergent to zero.
Bishop Nigel T.
Venter Liebrecht R.
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