Linearization Stability of Einstein Field Equations is a Generic Property

TL;DR

This paper proves that linearization stability is a generic property of Einstein field equations in certain space-times, meaning most such space-times are stable under small perturbations in a precise mathematical sense.

Contribution

It establishes that within a broad class of space-times, the subset of linearization stable solutions is open and dense, extending previous foundational work in the field.

Findings

Linearization stability is generic in the class of space-times with compact Cauchy hypersurfaces of constant mean curvature.

The subset of linearization stable space-times is open and dense in the $C^ abla$ topology.

The work builds upon and extends foundational results by Ebin, Fischer, Marsden, Moncrief, Beig, Chrusciel, and Schoen.

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 $[4]$.