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