The Cosmological Singularity

This book mathematically derives the theory underlying the Belinski–Khalatnikov–Lifshitz conjecture on the general solution of the Einstein equations with a cosmological singularity.

Vladimir Belinski (Author), Marc Henneaux (Author)

9781107047471, Cambridge University Press

Hardback, published 26 October 2017

278 pages, 10 b/w illus. 8 tables
26 x 18.5 x 2.1 cm, 0.66 kg

'This monograph discusses at length the structure of the general solution of the Einstein equations with a cosmological singularity in Einstein-matter systems in four and higher space-time dimensions, starting from the fundamental work of Belinski (the book's lead author), Khalatnikov and Lifshitz (BKL) - published in 1969. … Quite technical and advanced, this book is meant for theoretical and mathematical physicists working on general relativity, supergravity and cosmology.' CERN Courier

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.

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.

Subject Areas: Mathematical physics [PHU], Relativity physics [PHR]