Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-02-08
Class.Quant.Grav.26:165010,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Revised in response to referees' reports. Several minus sign errors corrected, and improved tables. Uses revtex4, 27 pages, 6
Scientific paper
10.1088/0264-9381/26/16/165010
Gravitational wave emission from extreme mass ratio binaries (EMRBs) should be detectable by the joint NASA-ESA LISA project, spurring interest in analytical and numerical methods for investigating EMRBs. We describe a discontinuous Galerkin (dG) method for solving the distributionally forced 1+1 wave equations which arise when modeling EMRBs via the perturbation theory of Schwarzschild blackholes. Despite the presence of jump discontinuities in the relevant polar and axial gravitational "master functions", our dG method achieves global spectral accuracy, provided that we know the instantaneous position, velocity, and acceleration of the small particle. Here these variables are known, since we assume that the particle follows a timelike geodesic of the Schwarzschild geometry. We document the results of several numerical experiments testing our method, and in our concluding section discuss the possible inclusion of gravitational self-force effects.
Field Scott E.
Hesthaven Jan S.
Lau Stephen R.
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