Production of massless particles in the de Sitter—Schwarzschild universe

The counterpart of the Teukolsky equation in the de Sitter---Schwarzschild universe (i.e., the radial part of the perturbed field equations) for massless fields of spin s=0, 1/2, 1, and 2 are considered with waves incident from the black-hole side on the cosmological horizon. In the limiting case of the mass of the black hole being small, we have derived an expression for the reflection coefficient. Here also, as in the de Sitter universe, the neutrino transmission coefficient is found to be zero.