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arXiv · 0802.4277

A new method to integrate (2+1)-wave equations with Dirac's delta functions as sources

Carlos O. Lousto·Hiroyuki Nakano
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Abstract

Unlike in the Schwarzschild black hole background, gravitational perturbations in a Kerr black hole background can not be decomposed into simple tensor harmonics in the time domain. Here, we make mode decompositions only in the azimuthal direction. As a first step, we discuss the resulting (2+1)-dimensional Klein-Gordon differential equation for scalar perturbations with a two dimensional Dirac's $δ$-function as a source representing a point particle orbiting a much larger black hole. To make this equation amenable for numerical integrations we explicitly remove analytically the singular behavior of the source and compute a global, well bahaved, effective source for the corresponding waveform.

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Carlos O. Lousto, Hiroyuki Nakano. 2008-04-21. A new method to integrate (2+1)-wave equations with Dirac's delta functions as sources. https://doi.org/10.1088/0264-9381%2F25%2F14%2F145018

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