The Cosmological Singularity

'The present monograph is a carefully developed overview about the mathematical details of the big bang singularity, mainly within (but not restricted to) general relativity theory. Chapter 1 presents the basic structure of the singularity, including the Kasner-like and the oscillatory-like cases. Chapters 2 and 3 deal with the Bianchi models, especially the BLK-cases Bianchi VIII and IX and the chaotic character observed there. In chapter 4, the influence of matter and/or changed space-time dimension are discussed. Chapters 5 and 6 deal with the billiard representation of the dynamical system describing the approach to the singularity by a mathematical equivalence of the system of equations to the motion of a point particle in a region with boundary, where (like in the billiard game), the article is reflected at the boundary. This idea is formalized in chapter 7 by the introduction of the Coxeter group. The appendices are useful for several topics, e.g., the spinor field and the Kac-Moody algebra.' Hans-Jürgen Schmidt, Zentralblatt MATH