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arXiv · 2010.15818

Characteristic formulation of the Regge-Wheeler and Zerilli Green functions

Conor O'Toole·Adrian Ottewill·Barry Wardell
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Abstract

We present a characteristic initial value approach to calculating the Green function of the Regge-Wheeler and Zerilli equations. We combine well-known numerical methods with newly derived initial data to obtain a scheme which can in principle be generalised to any desired order of convergence. We demonstrate the approach with implementations up to sixth-order in the grid spacing. By combining the results of our numerical code with late-time tail expansions and methods of subtracting the direct part of the Green function, we show that the scalar self-force in Schwarzschild spacetime can be computed to better accuracy than previous Green-function based approaches. We also demonstrate agreement with frequency-domain methods for computing the Green function in the gravitational case. Finally, we apply the Regge-Wheeler and Zerilli Green functions to the computation of the gravitational energy flux.

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Conor O'Toole, Adrian Ottewill, Barry Wardell. 2020-10-29. Characteristic formulation of the Regge-Wheeler and Zerilli Green functions. https://doi.org/10.1103/physrevd.103.124022

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