Exploring the gravitational stability / instability for a class of spacetime geometries

Abstract

In this thesis we review some of the ideas that come up while investigating the classical stability of spacetime geometries. We restrict to the case in which there is no matter. We derive all the necessary material from the first principles and assume an elementary knowledge of relativity theory on the part of the reader. Later on we generalise these ideas to investigate the stability / instability of higher dimensional Schwarzchild spacetimes (Schwarzchild-Tangherlini) under Ricci flow [19]. This is a part of an ongoing work. We also outline our basic strategy and suggest how we plan to proceed on the problem.