Characteristic formulation of the Regge-Wheeler and Zerilli Green functions

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.

v2. Added computation of gravitational flux. Added Zerilli Green function. Corrected typos, updated figures. 11 pages, 8 figures

References in corpus (9)

• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• Laser Interferometer Space Antenna
• Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves
• A recipe for echoes from exotic compact objects
• Intermediate mass-ratio black hole binaries: Applicability of small mass-ratio perturbation theory
• Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole
• Communication through quantum fields near a black hole
• Pade Approximants of the Green Function in Spherically Symmetric Spacetimes
• Regularized calculation of the retarded Green function in Schwarzschild spacetime

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