The aim of this section is to present a picture of the nature of
singularities in general solutions of the Einstein equations. It
is inspired by the ideas of Belinskii, Khalatnikov, and Lifshitz
(BKL). To fix ideas, consider the case of a solution of the
Einstein equations representing a cosmological model with a big
bang singularity. A central idea of the BKL picture is that near
the singularity the evolution at different spatial points
decouples. This means that the global spatial topology of the
model plays no role. The decoupled equations are ordinary
differential equations. They coincide with the equations for
spatially homogeneous cosmological models, so that the study of
the latter is of particular significance.