Towards adiabatic waveforms for inspiral into Kerr black holes: I. A new model of the source for the time domain perturbation equation

TL;DR

This paper introduces a new numerical method to model gravitational wave sources from particles orbiting Kerr black holes, improving accuracy and efficiency for waveform generation in inspiral studies.

Contribution

A novel technique to model the Dirac delta source term using minimal grid points, enabling efficient time-domain evolution of the Teukolsky equation for gravitational wave analysis.

Findings

Order of magnitude speed improvement over previous methods

Numerical errors less than 1% across parameter space

Effective modeling of the delta function with four grid points

Abstract

We revisit the problem of the emission of gravitational waves from a test mass orbiting and thus perturbing a Kerr black hole. The source term of the Teukolsky perturbation equation contains a Dirac delta function which represents a point particle. We present a technique to effectively model the delta function and its derivatives using as few as four points on a numerical grid. The source term is then incorporated into a code that evolves the Teukolsky equation in the time domain as a (2+1) dimensional PDE. The waveforms and energy fluxes are extracted far from the black hole. Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than 1% for a large fraction of parameter space. As a first application of this code, we analyze the effect of finite extraction radius on the energy fluxes. This paper is the first in a series whose goal is to develop adiabatic waveforms describing the inspiral of a small compact body into a massive Kerr black hole.