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Black Hole and Cosmological Particle Production in Schwarzschild de Sitter

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.