Properties of solutions to the mode equations for scalar fields in Schwarzschild-de Sitter spacetime

The behaviors of solutions to the mode equations for massless and massive scalar fields with minimal and conformal curvature couplings in Schwarzschild-de Sitter spacetime are investigated. Schwarzschild-de Sitter spacetime is an exact solution to Einstein's equations for a black hole in an expanding universe. It contains both a black hole horizon and a cosmological horizon. The focus will be on the region outside of the cosmological horizon.