Heun equation, Teukolsky equation, and type-D metrics

Starting with the whole class of type-D vacuum backgrounds with cosmological constant we show that the separated Teukolsky equation for zero rest-mass fields with spins s=+/- 2 (gravitational waves), s=+/- 1 (electromagnetic waves), and s=+/- 1/2 (neutrinos) is a Heun equation in disguise. (c) 2007 American Institute of Physics.