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We address some aspects of black hole spacetimes endowed with a positivecosmological constant, i.e. black holes located inside a cosmological eventhorizon. First we establish a general criterion for existence of cosmologicalevent horizons. Using the geometrical set up built for this, we study classicalblack hole no hair theorems for both static and stationary axisymmetricspacetimes. We discuss cosmic Nielsen-Olesen strings as hair inSchwarzschild-de Sitter spacetime. We also give a general calculation forparticle creation by a Killing horizon using complex path analysis and usingthis we study particle creation in Schwarzschild-de Sitter spacetime by bothblack hole and the cosmological event horizons.

Black holes and the positive cosmological constant