  We compute the spectra and total fluxes of quantum mechanically produced
particles crossing the black hole and cosmological horizons in Schwarzschild de
Sitter (SdS). Particle states are defined with respect to well-behaved, Kruskal
coordinates near the horizons, and as a consequence we find that these spectra
are generally non-thermal. The non-thermal Bogoliubov coefficient for a vacuum
fluctuation near the black hole horizon to produce a particle that crosses the
cosmological horizon is shown to equal to the convolution of two thermal
coefficients, one at the cosmological temperature and one at the black hole
temperature, weighted by the transmission coefficient for wave propagation in
static SdS coordinates. In this sense virtual thermal propagation underlies the
production process. This representation leads to the useful result that the
geometric optics approximation is reliable when used together with a low
frequency cut-off determined by the transmission coefficient. The large black
hole limit is a quasi-equilibrium situation as both temperatures approach the
common value of zero, the particle spectra become equal, and both emissions are
exponentially suppressed. Small black holes radiate as thermal bodies and
absorb a tiny flux of cosmological particles. The behavior of the quantum
fluctuations on the horizons is seen to be consistent with the Schottky anomaly
behavior of classical gravitational fluctuations.
