The Cosmological Singularity - Belinski, Vladimir

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Résumé :
This highly acclaimed series of monographs provides introductory accounts of specialised topics in mathematical physics for graduate students and research workers. The monographs in this series are of outstanding scholarship and written by those at the very frontiers of research. Subject areas covered include cosmology, astrophysics, relativity theory, particle physics, quantum theory, nuclear physics, statistical mechanics, condensed matter physics, plasma physics and the theory of chaos. 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, their billiard description, and emergent mathematical structures.

Biographie:
Vladimir Belinski holds a permanent professor position at the International Center for Relativistic Astrophysics Network, Italy. He is noted for his role in several key developments in theoretical physics, including the Belinski-Khalatnikov-Lifshitz conjecture on the behavior of generic solutions of Einstein equations near a cosmological singularity, the Belinski-Zakharov transform, and the Inflationary Attractor. He is co-author of the book Gravitational Solitons (Cambridge University Press, 2001) and has received the Landau Prize of the Russian Academy of Sciences (1974) and Marcel Grossmann Award (2012). Marc Henneaux is Full Professor at the Université Libre de Bruxelles and Director of the International Solvay Institutes for Physics and Chemistry. He has contributed significantly to understandings of gravity and black holes in three dimensions, and the geometrical and algebraic aspects of theories with a gauge freedom (in particular the Becchi-Rouet-Stora-Tyutin symmetry and its cohomology). He has received the Francqui Prize (2000), the Humboldt Prize (2009), the Bogoliubov Prize (2014), the FNRS Quinquennal Prize in Fundamental Exact Sciences (2015), and two ERC advanced grants (2011-2015 and 2016-2021).