Role of Topologies in the Study of Dynamical Aspects of Stable and Generic Properties of Space-times in General Relativity

TL;DR

This paper explores how different topologies and types of perturbations influence the stability and generic properties of space-times in general relativity, emphasizing the importance of these factors in understanding dynamical behaviors.

Contribution

It extends previous work by analyzing the impact of topology and perturbation nature on stability and discusses the genericity of linearization stability in space-times.

Findings

Topology and perturbation type are crucial for stability outcomes.

Linearization stability is shown to be a generic property.

Various stability aspects are discussed in different dynamical scenarios.

Abstract

In [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various situations in the dynamics of general relativity. We argue that not only choice of appropriate topology, but also the nature of perturbation, like metric, matter or initial data, are key factors in deciding whether a property is stable or not. We also study certain properties of space-times which are generic in an appropriate mathematical sense. In particular we argue that Linearization stability of a space-time is a generic property.