1205.1702 (David N. Pham)

Generalized de Sitter Space in $n$-dimensional Minkowski Space    [PDF]

David N. Pham

For $n\ge 3$, we study a particular class of hypersurfaces in $n$-dimensional Minkowski space which can be viewed as a generalization of de Sitter space. We show that every hypersurface in this class is diffeomorphic to $\mathbb{R}\times S^{n-2}$, and, we also give necessary and sufficient conditions for a hypersurface in this class to be timelike, null, or spacelike; in the non-null case, the hypersurface is shown to be a warped product. We then consider several examples from this class of hypersurfaces before constructing a spacetime which suppresses the "contraction" feature of ordinary de Sitter space while preserving the "expansion" feature.

View original: http://arxiv.org/abs/1205.1702