Numerical Evolution in time of curvature perturbations in Kerr black holes

TL;DR

This paper reviews the theory of curvature perturbations in Kerr black holes, focusing on evolving perturbations over time, the separability of solutions, and a numerical scheme for matter infall, with preliminary results presented.

Contribution

It introduces a numerical scheme for evolving Kerr perturbations over time and applies it to matter infall scenarios, advancing computational methods in black hole perturbation theory.

Findings

Separable solutions of the Teukolsky equation are described.

A numerical evolution scheme for Kerr perturbations is developed.

Preliminary results demonstrate the scheme's application to matter infall.

Abstract

This paper reviews the basic features of the theory of curvature perturbations in Kerr spacetime, which is customarily written in terms of gauge invariant components of the Weyl tensor which satisfy a perturbation equation known as the Teukolsky equation. I will describe how to evolve generic perturbations about the Kerr metric and the separable form of the wave solutions that one obtains, and the relation of the Teukolsky function to the energy of gravitational waves emitted by the black hole. A discussion of a numerical scheme to evolve perturbations as a function of time and some preliminary results of our research project implementing it for matter sources falling into the black hole is included.