Effects of a nonvanishing cosmological constant on the spherically symmetric vacuum manifold

Abstract

The conformal structure of timelike 2-surfaces of the vacuum manifold is examined in detail in the cases when the cosmological constant, $\lambda$, is not assumed to be zero. For $\lambda >0\mathrm{}$ with $3m\le {\Lambda }^{-\frac{1}{2}}$ it is shown that these surfaces constitute the junction of an infinite number of regions and that the complete manifold may be represented in a causal way by a finite number of regions.