Stability and Genericity Aspects of Properties of Space-times in General Relativity

TL;DR

This paper reviews the stability and genericity of certain properties of space-times in General Relativity, emphasizing linearization stability as a generic property under specific conditions.

Contribution

It provides a comprehensive discussion on stability and genericity, and argues that linearization stability is generic for space-times with compact spacelike constant mean curvature hypersurfaces.

Findings

Linearization stability is generic in certain classes of space-times.

Discussion on various aspects of stability and genericity in General Relativity.

Supports the conclusion with theoretical arguments.

Abstract

In this article, we review and discuss different aspects of stability and genericity of some properties of space-times which occur in various contexts in the General Theory of Relativity. We also give argument supporting the conclusion that Linearization Stability is a generic property if we restrict space-times to the class of those which admit compact spacelike constant mean curvature hypersurfaces.