Stability by linearization of Einstein’s equation, general concepts

The stability by linearization of Einstein’s equation in the vacuum has been widely studied in the literature (refs. [22], [23], [32], [34], [2], [49], [52]). In [50] an interesting bibliography on the subject may be found. The same concept for Einstein’s equation in the presence of matter has been studied in [14] and [16] for Robertson-Walker cosmological models. In sections V.1, V.2 and V.3 we will provide the reader with the general concepts concerning stability by linearization of Einstein’s equation, in the vacuum as well as in the presence of matter. Section V.5 is devoted to clarifying a technical question concerning Sobolev spaces, and finally Section V.6 covers some calculus needed in the following chapters. © 2010, Birkhäuser, Springer Basel AG.