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

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 $\delta$-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.

18 pages, 6 figures, Some comments added

References in corpus (4)

• Further insight into gravitational recoil
• Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals
• Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in 2+1 dimensions
• m-Mode Regularization Scheme for the Self Force in Kerr Spacetime