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Cosmological Singularity [Kietas viršelis]

(Université Libre de Bruxelles),
  • Formatas: Hardback, 278 pages, aukštis x plotis x storis: 260x185x21 mm, weight: 660 g, 8 Tables, black and white; 5 Halftones, black and white; 5 Line drawings, black and white
  • Serija: Cambridge Monographs on Mathematical Physics
  • Išleidimo metai: 26-Oct-2017
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107047471
  • ISBN-13: 9781107047471
Kitos knygos pagal šią temą:
Cosmological SingularityDidesnis paveikslėlis
  • Formatas: Hardback, 278 pages, aukštis x plotis x storis: 260x185x21 mm, weight: 660 g, 8 Tables, black and white; 5 Halftones, black and white; 5 Line drawings, black and white
  • Serija: Cambridge Monographs on Mathematical Physics
  • Išleidimo metai: 26-Oct-2017
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107047471
  • ISBN-13: 9781107047471
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781107047471.html
Raktažodžiai:
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 conjecture on this area of research.

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.

Recenzijos

'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 '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

Daugiau informacijos

This book mathematically derives the theory underlying the BelinskiKhalatnikovLifshitz conjecture on the general solution of the Einstein equations with a cosmological singularity.
Preface xi
Acknowledgements xiii
Introduction 1(4)
Part I BKL Analysis
5(90)
1 Basic Structure of Cosmological Singularity
7(25)
1.1 Synchronous Reference System
7(2)
1.2 The Gravitational Field Equations
9(1)
1.3 General Solution
10(1)
1.4 Definition of Cosmological Singularity
11(2)
1.5 Kasner-Like Singularities of Power Law Asymptotics
13(4)
1.6 Instability of Kasner Dynamics
17(3)
1.7 Transition to the New Regime
20(4)
1.8 Oscillatory Nature of the Generic Singularity
24(3)
1.9 Rotation of Kasner Axes
27(3)
1.10 Final Comments
30(2)
2 Homogeneous Cosmological Models
32(16)
2.1 Homogeneous Models of Bianchi Types IX and VIII
32(1)
2.2 Equations of Motion for Homogeneous Models
33(5)
2.3 Models of Types IX and VIII with Fixed Kasner Axes
38(3)
2.4 Models of Types IX and VIII with Rotating Axes
41(5)
2.5 On the Extension to the Inhomogeneous Case
46(2)
3 On the Cosmological Chaos
48(9)
3.1 Stochasticity of the Oscillatory Regime
48(3)
3.2 Historical Remarks
51(2)
3.3 Gravitational Turbulence
53(4)
4 On the Influence of Matter and Space-Time Dimension
57(38)
4.1 Introduction
57(4)
4.2 Perfect Fluid
61(4)
4.3 Perfect Fluid of Stiff Matter Equation of State
65(6)
4.4 Yang-Mills and Electromagnetic Fields
71(9)
4.5 Scalar Field
80(1)
4.6 Pure Gravity in Higher Dimensions
81(6)
4.7 Generalized Kasner Solutions: Rigorous Results
87(1)
4.8 On the Influence of Viscous Matter
88(7)
Part II Cosmological Billiards
95(106)
5 The Billiard of Four-Dimensional Vacuum Gravity
97(48)
5.1 Hamiltonian Form of the Action
97(2)
5.2 Supermetric
99(5)
5.3 More on Hyperbolic Space H2
104(5)
5.4 Kasner Solution Revisited
109(7)
5.5 Hamiltonian in Pseudo-Gaussian Gauge
116(4)
5.6 BKL Limit and Emergence of Billiard Description
120(7)
5.7 Collision Law
127(5)
5.8 Miscellanea
132(4)
5.9 Chaos and Volume of the Billiard Table
136(2)
5.10 Coxeter Group for Pure Gravity in Four Dimensions
138(7)
6 General Cosmological Billiards
145(25)
6.1 Models --- Hamiltonian Form of the Action
145(3)
6.2 Geometry of the Space of Scale Factors
148(6)
6.3 Hyperbolic Space in M Dimensions
154(4)
6.4 Hamiltonian in Iwasawa Variables and BKL Limit
158(3)
6.5 Walls
161(4)
6.6
Chapter 4 Revisited
165(2)
6.7 Miscellanea
167(3)
7 Hyperbolic Coxeter Groups
170(31)
7.1 Introduction
170(1)
7.2 Convex Polyhedra in Hyperbolic Space
171(3)
7.3 Coxeter Groups: General Considerations
174(2)
7.4 Coxeter Groups: Examples
176(6)
7.5 Coxeter Groups and Weyl Groups
182(6)
7.6 Coxeter Groups Associated with Gravitational Theories
188(10)
7.7 The Kac--Moody Symmetry Conjecture
198(3)
Appendices
201(2)
A Various Technical Derivations
203(10)
A.1 Perturbations to Kasner-Like Asymptotics
203(2)
A.2 Frame Components of the Ricci Tensor
205(1)
A.3 Exact Solution for Transition Between Two Kasner Epochs
206(2)
A.4 The Derivation of the Rotation Effect of the Kasner Axes
208(5)
B Homogeneous Spaces and Bianchi Classification
213(8)
B.1 Homogeneous Three-Dimensional Spaces
213(2)
B.2 Bianchi Classification
215(2)
B.3 Frame Vectors
217(2)
B.4 On the Freezing Effect in Bianchi IX Model
219(2)
C Spinor Field
221(10)
C.1 Equations of the Gravitational and Spinor Fields
222(2)
C.2 An Exact Homogeneous Solution for the Massless Case
224(4)
C.3 The General Solution in the Vicinity of the Singularity
228(3)
D Lorentzian Kac--Moody Algebras
231(21)
D.1 Definitions
231(2)
D.2 Roots
233(1)
D.3 The Chevalley Involution
234(1)
D.4 Three Examples
234(2)
D.5 The Affine Case
236(1)
D.6 The Invariant Bilinear Form
237(3)
D.7 The Weyl Group
240(3)
D.8 Hyperbolic Kac--Moody Algebras
243(4)
D.9 Overextensions of Finite-Dimensional Lie Algebras
247(5)
References 252(9)
Index 261
Vladimir Belinski holds a permanent professor position at the International Center for Relativistic Astrophysics Network (ICRANet), Italy. He is noted for his role in several key developments in theoretical physics, including the BelinskiKhalatnikovLifshitz conjecture on the behavior of generic solutions of Einstein equations near a cosmological singularity, the BelinskiZakharov transform, and the 'Inflationary Attractor'. He is co-author of the book Gravitational Solitons (Cambridge, 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 BecchiRouetStoraTyutin symmetry and its cohomology). He has received the Francqui Prize (2000), the Humboldt Prize (2009), the Bogoliubov Prize (2014), the Fonds National de La Recherche Scientifique (FNRS) Quinquennal Prize in Fundamental Exact Sciences (2015), and two ERC advanced grants (20112015 and 20162021).