8 Structure of General Singularities
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