The results on strong cosmic censorship in Gowdy vacuum spacetimes cover the polarized sub-case as well
as the general T^{3}-Gowdy case. However, to the best of our knowledge, there are no results concerning
strong cosmic censorship in the general S^{3} and S^{2} × S^{1} cases. The method of proof, in all the situations in
which results exist, consists of a detailed analysis of the asymptotics of solutions. As a consequence, we shall
devote most of this review to a description of the analysis of the asymptotic behavior. Note that it might be
possible to prove strong cosmic censorship without analyzing the asymptotics in detail. In fact, there are
proofs under related symmetry assumptions, which are not based on a detailed analysis of the
asymptotics [25, 26, 27, 84].

The existence of asymptotic expansions in the direction towards the singularity has played a central
role in proving strong cosmic censorship for T^{3} and polarized vacuum Gowdy spacetimes. In
the latter case, to take one example, there is a computation of asymptotic expansions due to
Isenberg and Moncrief [50]. This computation was then used in [21] in the proof of strong
cosmic censorship in the polarized case. In the general T^{3}-case, there is a large literature on
asymptotic expansions, which we shall return to in Section 8; the starting point being the work of
Grubišić and Moncrief [40]. It is worth noting that both in the case of [40] and [50], the ideas of
Belinskii, Khalatnikov, and Lifshitz [55, 6, 7] (henceforth BKL) played an important role. As a
consequence, we wish to give a brief description of the BKL perspective as well as of some related
proposals.

5.1 The BKL picture

5.2 Asymptotic expansions, Fuchsian methods

5.2.1 From solutions to asymptotics

5.2.2 From asymptotics to solutions

5.2.3 Overview of results

5.2 Asymptotic expansions, Fuchsian methods

5.2.1 From solutions to asymptotics

5.2.2 From asymptotics to solutions

5.2.3 Overview of results

http://www.livingreviews.org/lrr-2010-2 |
This work is licensed under a Creative Commons License. Problems/comments to |