Construction of Hyperboloidal Initial Data Using Pseudo-Spectral Methods

Details Construction of Hyperboloidal Initial Data Using Pseudo-Spectral Methods Construction of Hyperboloidal Initial Data Using Pseudo-Spectral Methods

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet.1697f&link_type=abstract

"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R

Physics

Scientific paper

We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable conformal factor which transforms an initial data set in physical space-time to the ambient conformal completion. This is achieved by solving the Yamabe equation, a nonlinear second order equation. The second step is the computation of the Ricci and Weyl curvature on the initial hypersurface. This step involves a division by the conformal factor which vanishes at null-infinity. Both parts are treated pseudo-spectrally. These data can be used to generate general relativistic space-times by evolution with the conformal equations.

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