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We study the quasinormal mode eigenvalues and eigenfunctions for theTeukolsky 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 theTeukolsky equation are regular from the black hole horizon to future nullinfinity in these coordinates. We then present several example quasinormaleigenfunction solutions, and study some of their properties in thenear-extremal Kerr limit.

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