Non-genericity of the Nariai solutions: I. Asymptotics and spatially homogeneous perturbations

Understand

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.