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 $[4]$.