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GR: Fachverband Gravitation und Relativitätstheorie

GR 9: Numerische Relativitätstheorie I

GR 9.6: Talk

Wednesday, February 27, 2013, 15:15–15:30, HS 6

Spectral time evolution of wave equations on hyperboloidal slices — •Rodrigo Panosso Macedo and Marcus Ansorg — Theoretical Physics Institute - University of Jena, Jena, Germany

We present a new numerical scheme for the time evolution of axi-symmetric wave equations around a black hole. The code relies on two features: i) the surfaces of constant time extend all the way towards future null infinity (hyperboloidal slices), which is included in the computational domain by a compactification of the radial coordinate, ii) the wave equations are solved by means of a pseudo-spectral method, which is applied here to both spatial and time directions. The inversion of the resulting dense matrix is efficiently performed with a specifically designed iterative method. We obtain extreme precision of the numerical solution close to machine accuracy, which allows us to study in detail the field's tail, i.e., the decay as an inverse power law in the asymptotic time evolution.