Linearization Stability of Einstein Field Equations is a Generic Property

Abstract

In this paper, we prove that Linearization Stability of Einstein Field Equations is a Generic Property in the sense that within the class $\mathcal{V}$ of space-times which admit a compact Cauchy hypersurface of constant mean curvature, the subclass ${\mathcal{V}}_K$ of space-times which are linearization stable forms an open and dense subset of $\mathcal{V}$ under $C^{\infty }$ - topology. The work is based upon the work of Ebin $[1]$, Fischer, Marsden and Moncrief $[2,3]$ and Beig, Chrusciel and Schoen $[4]$.

11 pages, comments are welcome

References in corpus (2)

• A Note on the Topology of a Generic Subspace of Riem
• Metrics without isometries are generic