Stability by linearization of Einstein’s equation in Robertson-Walker cosmological models

This chapter will deal with a study of stability by linearization of Einstein’s equation when the initial metric and the initial stress-energy tensor are those from a Robertson-Walker cosmological model. If we interpret the universe as a Robertson-Walker model with metric (Formula Presented.) and stress-energy tensor T, the explosion of a supernova in a distant galaxy will produce a perturbation of the initial stress-energy tensor T which will give rise to a perturbation of the initial metric (Formula Presented.). The perturbed universe will no longer be of Robertson-Walker type. In order to study the effects of this explosion, is it correct or not to work with a linearized Einstein equation? An important role in answering this question is played by the new concept of stability by linealization introduced in Section V.2, since we do not deal here with the case of linearization of Einstein’s equation in the vacuum: we have to linearize it in presence of the matter. The authors of this monograph have just studied this case in [14], [15] and [16]. © 2010, Birkhäuser, Springer Basel AG.