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

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Cited by in corpus (10)

• The motion of point particles in curved spacetime
• Gravitational self force in extreme mass-ratio inspirals
• Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
• Self force on a scalar charge in Kerr spacetime: circular equatorial orbits
• An Efficient Pseudospectral Method for the Computation of the Self-force on a Charged Particle: Circular Geodesics around a Schwarzschild Black Hole
• Pseudospectral Collocation Methods for the Computation of the Self-Force on a Charged Particle: Generic Orbits around a Schwarzschild Black Hole
• New Kludge Scheme for the Construction of Approximate Waveforms for Extreme-Mass-Ratio Inspirals
• Self force via m-mode regularization and 2+1D evolution: Foundations and a scalar-field implementation on Schwarzschild
• Generic effective source for scalar self-force calculations
• Self-force: Computational Strategies