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

Abstract

We study the quasinormal modes and eigenfunctions for the Kerr spacetime in a horizon penetrating, hyperboloidally compactified (HPHC) coordinate system. Following earlier work by Zenginoglu [1], we show that the physical 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 eigenfunction solutions, and study some of their properties in near-extremal Kerr limit.