Asymptotic Singular Behavior of Inhomogeneous Spacetimes in String Theory

In 1960's Penrose, Hawking and Geroch have shown that singularities are a general future of classes of solutions to Einstein's equations. Unfortunately, their results said nothing about the structure of those singularities. In 1970's Belinskii, Khalatnikov and Lifshitz (BKL) have given a heuristic description of singularities ⁴. They investigated how the spacetime evolves into the singularity and conjectured that the dynamics of nearby observers would decouple near singularities. (the BKL conjecture.) Then, BKL further speculated that a generic singularity should be locally behaved like a Mixmaster type ("oscillatory approach to the singularity")...