Computing the quasinormal modes and eigenfunctions for the Teukolsky equation using horizon penetrating, hyperboloidally compactified coordinates

TL;DR

This paper computes quasinormal modes and eigenfunctions of the Teukolsky equation using horizon penetrating, hyperboloidally compactified coordinates, demonstrating regularity from the horizon to infinity and exploring properties near extremal Kerr black holes.

Contribution

It introduces a method to compute quasinormal modes in HPHC coordinates, ensuring regularity across the black hole horizon and extending analysis to near-extremal Kerr black holes.

Findings

Eigenfunctions are regular from horizon to null infinity in HPHC coordinates.

Several example solutions of quasinormal modes are presented.

Properties of eigenfunctions are analyzed in the near-extremal Kerr limit.

Abstract

We study the quasinormal mode eigenvalues and eigenfunctions for the Teukolsky equation in a horizon penetrating, hyperboloidally compactified (HPHC) coordinate system. Following earlier work by Zengino\u{g}lu (arXiv:1102.2451), we show that the quasinormal eigenfunctions for the Teukolsky equation are regular from the black hole horizon to future null infinity in these coordinates. We then present several example quasinormal eigenfunction solutions, and study some of their properties in the near-extremal Kerr limit.