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

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

2008-02-28

arxiv.org/abs/0802.4277v2

Class.Quant.Grav.25:145018,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, 6 figures, Some comments added

Scientific paper

10.1088/0264-9381/25/14/145018

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 $\delta$-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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