One dimensional description of the gravitational perturbation in a Kerr background

TL;DR

This paper simplifies the analysis of gravitational perturbations in Kerr black holes by reducing the problem to a one-dimensional harmonic equation, especially effective for low-spin cases, aiding waveform generation.

Contribution

It introduces a method to approximate Kerr perturbations with a single mode equation, demonstrating weak mode coupling and improving computational efficiency.

Findings

Dominant mode corresponds to initial perturbation mode.

Weak coupling among modes allows for simplified equations.

Accurate waveforms can be generated efficiently for low-spin Kerr black holes.

Abstract

The perturbation equation in a Kerr background is written as a coupled system of one dimensional equations for the different modes in the time domain. Numerical simulations show that the dominant mode in the gravitational response is the one corresponding to the mode of the initial perturbation, allowing us to conjecture that the coupling among the modes has a weak influence in our system of equations. We conclude that by neglecting the coupling terms it can be obtained a one dimensional harmonic equation which indeed describes with good accuracy the gravitational response from the Kerr black hole with low spin, while only few couplings are necessary to describe a high spin one. This result may help to understand the structure of test fields in a Kerr background and even to generate accurate waveforms for various cases in an efficient manner.