Rotating black hole in asymptotic de Sitter space: Perturbation of the space-time with spin fields

The Newman-Penrose formalism is used to work with gravitational, electromagnetic, and Dirac field perturbations of the Kerr—de Sitter space. It is shown that the resulting equations are separable, and the radial parts (for the massless fields) combine into a master equation resembling that of Teukolsky. This master equation includes the Teukolsky equation and the equation arising from the de Sitter-Schwarzschild universe, and can be reduced to these cases under appropriate limiting conditions. Finally, the radial parts of the electromagnetic and neutrino fields are transformed to the form of the one-dimensional barrier-penetration equation.