  This is the first of two papers where we study the asymptotics of the
generalized Nariai solutions and its relation to the cosmic no-hair conjecture.
According to the cosmic no-hair conjecture, generic expanding solutions of
Einstein's field equations in vacuum with a positive cosmological constant
isotropize and approach the de-Sitter solution asymptotically. The family of
solutions which we introduce as "generalized Nariai solutions", however, shows
quite unusual asymptotics and hence should be non-generic in some sense. In
this paper, we list basic facts for the Nariai solutions and characterize their
asymptotic behavior geometrically. One particular result is a rigorous proof of
the fact that the Nariai solutions do not possess smooth conformal boundaries.
We proceed by explaining the non-genericity within the class of spatially
homogeneous solutions. It turns out that perturbations of the three isometry
classes of generalized Nariai solutions are related to different mass regimes
of Schwarzschild de-Sitter solutions. A motivation for our work here is to
prepare the second paper devoted to the study of the instability of the Nariai
solutions for Gowdy symmetry. We will be particularly interested in the
construction of new and in principle arbitrarily complicated cosmological black
hole solutions.
