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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/200286Unlike 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.18 pages, 6 figures, Some comments addedGeneral Relativity and Quantum CosmologyAstrophysicsA new method to integrate (2+1)-wave equations with Dirac's delta functions as sourcestext