Scattering amplitudes and thermal temperatures of the Schwarzschild-de Sitter black holes

We study thermodynamic evaporation of Schwarzschild-de Sitter black holes in terms of a low energy perturbation theory. A small black hole which is far from the cosmological horizon and observers at the spacelike hypersurface where black hole attraction and expansion of cosmological horizon balance exactly are considered. In the low energy perturbation, scalar field equations are solved in both regions of the hypersurface and scattering amplitudes are derived. Then the desired thermal temperatures from the two horizons are obtained as a "minimal" value of the statistical thermal temperature, and the fine tuning between amplitudes gives a relation between the two temperatures.