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We study quantum mechanical and classical stability properties ofReissner-Nordstrom deSitter spacetimes, which describe black holes with mass$M$ and charge $Q$ in a background with cosmological constant $\Lambda \ge 0$.There are two sources of particle production in these spacetimes; the blackhole horizon and the cosmological horizon. A scattering calculation is done tocompute the Hawking radiation in these spacetimes. We find that the flux fromthe black hole horizon equals the flux from the cosmological horizon, if andonly if $|Q|=M$, indicating that this is a state of thermodynamic equilibrium.The spectrum, however, is not thermal. We also show that spacetimes containinga number of charge equal to mass black holes with $\Lambda \ge 0$, havesupercovariantly constant spinors, suggesting that they may be minimum energystates in a positive energy construction. As a first step in this direction, wepresent a positive energy construction for asymptotically deSitter spacetimeswith vanishing charge. Because the construction depends only on a spatialslice, our result also holds for spacetimes which are asymptoticallyRobertson-Walker.Comment: 11 pages (1 figure not included), UMHEP-39

Particle production and positive energy theorems for charged black holes in DeSitter