Analysis of the generic singularity studies by Belinskii, Khalatnikov, and Lifschitz.

We apply some modern mathematical methods of global analysis to a series of studies undertaken by Belinskii, Khalatnikov and Lifschitz (BKL) to elucidate the structure of space-time near a general cosmological singularity. A brief summary of BKL's large body of work on inhomogeneous cosmological models is given (their work on homogeneous models is not under discussion here). Various theorems are proven and analyses of a mathematical and physical nature are made to show that the constructions of BKL cannot be general and in some cases do not give Lorentz manifolds. We conclude that although the work of BKL has led to very significant advances in our understanding of the dynamics of homogeneous cosmological models, the local techniques they employ do not extend to give us reliable information about the global structure of generic space-times. A detailed discussion of stability, generality, function counting, linearization stability, physical singularities and fictitious singularities is given together with an outline of various physical considerations which might be useful in future studies of the structure of generic space-times.