  The Euclidean Schwarzschild-de Sitter geometry may be considered as an
extremum of two different action principles. If the thermodynamical parameters
are held fixed at the cosmological horizon, one deals with the gravitational
thermodynamical effects of the black hole but ignores those of the cosmological
horizon. Conversely, if the macroscopical variables are held fixed at the black
hole horizon, it is only the cosmological horizon thermodynamics which is dealt
with. Both cases are analyzed. In particular, the internal energy U is
calculated in the semiclassical approximation as a function of the mass
parameter m of Schwarzschild de Sitter space. In the first case one finds U=+m,
while in the second one gets U=-m. This suggests that de Sitter space is
thermodynamically unstable under black hole formation.
