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Full Description
Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski-Khalatnikov-Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singularities, the billiard description, and emergent mathematical structures.
Contents
Preface; 1. Introduction and outline; Part I. BKL Analysis: 2. Basic structure of cosmological singularity; 3. Homogeneous cosmological models; 4. On the cosmological chaos; 5. On the Inuence of matter and spacetime dimension; Part II. Cosmological Billiards: 6. The billiard of four-dimensional vacuum gravity; 7. General Cosmological Billiards; 8. Hyperbolic Coxeter groups; Appendix A. Various technical derivations; Appendix B. Homogeneous spaces and Bianchi classification; Appendix C. Spinor field; Appendix D. Lorentzian Kac-Moody algebras; References; Index.
