  We present a method for determining the purely imaginary quasinormal modes of
the Kerr geometry. Such modes have previously been explored, but we show that
prior results are incorrect. The method we present, based on the theory of Heun
polynomials, is very general and can be applied to a broad class of problems,
making it potentially useful to all branches of physics. Furthermore, our
application provides an example where the method of matched asymptotic
expansions seems to have failed. A deeper understanding of why it fails in this
case may provide useful insights for other situations.
