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

Carlos O Lousto, Hiroyuki Nakano
2008 Classical and quantum gravity  
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
more » ... er 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.
doi:10.1088/0264-9381/25/14/145018 fatcat:4rvjaegbpzhkvezrgrvcssu3i4