The Springer Handbook Of Spacetime Is Dedicated To The Ground-breaking Paradigm Shifts Embodied In The Two Relativity Theories, And Describes In Detail The Profound Reshaping Of Physical Sciences They Ushered In. It Includes In A Single Volume Chapters On Foundations, On The Underlying Mathematics, On Physical And Astrophysical Implications, Experimental Evidence And Cosmological Predictions, As Well As Chapters On Efforts To Unify General Relativity And Quantum Physics. The Handbook Can Be Used As A Desk Reference By Researchers In A Wide Variety Of Fields, Not Only By Specialists In Relativity But Also By Researchers In Related Areas That Either Grew Out Of, Or Are Deeply Influenced By, The Two Relativity Theories: Cosmology, Astronomy And Astrophysics, High Energy Physics, Quantum Field Theory, Mathematics, And Philosophy Of Science. It Should Also Serve As A Valuable Resource For Graduate Students And Young Researchers Entering These Areas, And For Instructors Who Teach Courses On These Subjects. The Handbook Is Divided Into Six Parts. Part A: Introduction To Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure And Mathematics. Part D: Confronting Relativity Theories With Observations. Part E: General Relativity And The Universe. Part F: Spacetime Beyond Einstein. Key Topics › Historical Origins Of The Spacetime Notion › Basic Ideas Of Special And General Relativity › Nature Of Time And Gravity › Mathematical Structures › Physical And Astrophysical Implications › Observational Status Of The Two Relativity Theories, › Various Approaches To Unify General Relativity And Quantum Physics. Features › Concise, Clear And Coherent Presentation › Research And Application-oriented › Includes Recent Developments › Exhaustive References To Approved Data › All Chapters With Summaries › A Resourse For Graduate Students, Researchers And Teachers In The Field Introduction To Spacetime Structure -- Foundational Issues -- Spacetime Structure And Mathematics -- Confronting Relativity Theories With Observations -- General Relativity And The Universe -- Spacetime Beyond Einstein. Edited By Abhay Ashtekar, Vesselin Petkov.

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Abhay Ashtekar, Vesselin Petkov (eds.)

Ashtekar, Abhay; Petkov, Vesselin

Spektrum Akademischer Verlag. in Springer-Verlag GmbH

Steinkopff. in Springer-Verlag GmbH

Springer London, Limited

EBL-Schweitzer, Online-ausg, Berlin, Heidelberg, 2014

Springer Nature, Berlin, 2014

Dordrecht [Germany, 2014

Springer Handbooks, 2014

Berlin, cop. 2014

Germany, Germany

2014, PS, 2014

Sep 10, 2014

Mobilism

sm28939156

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Source title: Springer Handbook of Spacetime (Springer Handbooks)

Preface
About the Editors
List of Authors
Contents
List of Abbreviations
Part A Introduction to Spacetime Structure
1 From Æther Theory to Special Relativity
1.1 Space and Time in Classical Mechanics
1.2 Relativity in Classical Mechanics
1.3 The Theory of Light and Absolute Motion
1.4 Einstein's Special Relativity
1.5 Relativistic Mechanics
1.6 Conclusion
References
2 The Historical Origins of Spacetime
2.1 Poincaré's Theory of Gravitation
2.2 Minkowski's Path to Spacetime
2.3 Spacetime Diagrams
References
3 Relativity Today
3.1 Operational Definitions
3.2 Lorentz Transformations in Two Dimensions
3.3 Inertial Coordinates in Four Dimensions
3.4 Vectors
3.5 Proper Time
3.6 Four-Acceleration
3.7 Visual Observation
3.8 Operational Definition of Mass
3.9 Maxwell's Equations
References
4 Acceleration and Gravity: Einstein's Principle of Equivalence
4.1 Prologue
4.2 The Role of the Equivalence Principle in General Relativity
4.3 Experimental Tests
4.4 Relativistic Definition of Acceleration
4.5 Accelerating Frame in Minkowski Spacetime
4.6 Concluding Remarks
References
5 The Geometry of Newton's and Einstein's Theories
5.1 Guide to Chapter
5.2 Geometry
5.3 Newtonian Mechanics I
5.4 Newtonian Mechanics II
5.5 Special Relativity
5.6 Absolute and Dynamical Variables; Covariance
5.7 General Relativity
5.8 Cosmology
References
6 Time in Special Relativity
6.1 The Spacetime of Prerelativistic Physics
6.2 The Spacetime Structure of Special Relativity
6.3 Philosophical Issues
References
Part B Foundational Issues
7 Rigid Motion and Adapted Frames
7.1 Rigid Rod in Special Relativity
7.2 Frame for an Accelerating Observer
7.3 General Motion of a Continuous Medium
7.4 Rigid Motion of a Continuous Medium
7.5 Rate of Strain Tensor
7.6 Examples of Rigid Motion
7.7 Rigid Motion Without Rotation
7.8 Rigid Rotation
7.9 Generalized Uniform Acceleration and Superhelical Motions
7.10 A Brief Conclusion
References
8 Physics as Spacetime Geometry
8.1 Foundational Knowledge and Reality of Spacetime
8.2 Four-Dimensional Physics as Spacetime Geometry
8.3 Propagation of Lightin Noninertial Reference Frames in Spacetime
References
9 Electrodynamics of Radiating Charges in a Gravitational Field
9.1 The Dynamics of a Charged Particle
9.2 Schott Energy as Electromagnetic Field Energy
9.3 Pre-Acceleration and Schott Energy
9.4 Energy Conservation During Runaway Motion
9.5 Schott Energy and Radiated Energy of a Freely Falling Charge
9.6 Noninvariance of Electromagnetic Radiation
9.7 Other Equations of Motion
9.8 Conclusion
References
10 The Nature and Origin of Time-Asymmetric Spacetime Structures
10.1 The Time Arrow of Gravitating Systems
10.2 Black Hole Spacetimes
10.3 Thermodynamicsand Fate of Black Holes
10.4 Expansion of the Universe
10.5 Quantum Gravity
References
11 Teleparallelism: A New Insight into Gravity
11.1 Preliminaries
11.2 Basic Concepts
11.3 Teleparallel Gravity: A Brief Review
11.4 Achievements of Teleparallel Gravity
11.5 Final Remarks
References
12 Gravity and the Spacetime: An Emergent Perspective
12.1 Introduction, Motivation, and Summary
12.2 Curious Features in the Conventional Approach to Classical Gravity
12.3 Quantum Theoryand Spacetime Horizons
12.4 Gravitational Dynamicsand Thermodynamics of Null Surfaces
12.5 Gravity from an Alternative Perspective
12.6 Emergence of Cosmic Space
12.7 A Principle to Determine the Value of the Cosmological Constant
12.8 Conclusions
References
13 Spacetime and the Passage of Time
13.1 Spacetime and the Block Universe
13.2 Time and the Emerging Block Universe
13.3 A Problem: Surfaces of Change
13.4 Other Arguments Against an EBU
13.5 Time with an Underlying Timeless Substratum
13.6 It's All in the Mind
13.7 Taking Delayed Choice Quantum Effects into Account
13.8 The Arrow of Timeand Closed Time-Like Lines
13.9 Overall: A More Realistic View
13.A The ADM Formalism
References
14 Unitary Representations of the Inhomogeneous Lorentz Group and Their Significance in Quantum Physics
14.1 Lorentz Invariance in Quantum Theory
14.2 Wigner's Heuristic Derivation of the Projective Representations of the Inhomogeneous Lorentz Group
14.3 On Mackey's Theory of Induced Representations
14.4 Free Classical and Quantum Fields for Arbitrary Spin, Spin, and Statistics
14.A Appendix: Some Key Points of Mackey's Theory
References
Part C Spacetime Structure and Mathematics
15 Spinors
15.1 Spinor Basics
15.2 Manipulating Spinors
15.3 Groups; Representations
15.4 Spinor Structure
15.5 Lie and Other Derivatives
15.6 4-Spinors
15.7 Euclidean Spinors
15.8 Bases; Spin Coefficients
15.9 Variations Involving Spinors
References
16 The Initial Value Problem in General Relativity
16.1 Overview
16.2 Derivation of the Einstein Constraint and Evolution Equations
16.3 Well-Posedness of the Initial Value Problem for Einstein's Equations
16.4 The Conformal Method and Solutions of the Constraints
16.5 The Conformal Thin Sandwich Method
16.6 Gluing Solutions of the Constraint Equations
16.7 Comments on Long-Time Evolution Behavior
References
17 Dynamical and Hamiltonian Formulation of General Relativity
17.1 Overview
17.2 Notation and Conventions
17.3 Einstein's Equations
17.4 Spacetime Decomposition
17.5 Curvature Tensors
17.6 Decomposing Einstein's Equations
17.7 Constrained Hamiltonian Systems
17.8 Hamiltonian GR
17.9 Asymptotic Flatness and Charges
17.10 Black-Hole Data
17.11 Further Developments, Problems, and Outlook
References
18 Positive Energy Theorems in General Relativity
18.1 Theorems
18.2 Energy
18.3 Linear Momentum
18.4 Proof
18.5 Further Results and Open Problems
References
19 Conserved Charges in Asymptotically (Locally) AdS Spacetimes
19.1 Asymptotically Locally AdS Spacetimes
19.2 Variational Principles and Charges
19.3 Relation to Hamiltonian Charges
19.4 The Algebra of Boundary Observables and the AdS/CFT Correspondence
References
20 Spacetime Singularities
20.1 Space, Time and Matter
20.2 What Is a Singularity?
20.3 Gravitational Focusing
20.4 Geodesic Incompleteness
20.5 Strong Curvature Singularities
20.6 Can We Avoid Spacetime Singularities?
20.7 Causality Violations
20.8 Energy Conditionsand Trapped Surfaces
20.9 Fundamental Implications and Challenges
20.10 Gravitational Collapse
20.11 Spherical Collapse and the Black Hole
20.12 Cosmic Censorship Hypothesis
20.13 Inhomogeneous Dust Collapse
20.14 Collapse with General Matter Fields
20.15 Nonspherical Collapse and Numerical Simulations
20.16 Are Naked Singularities Stable and Generic?
20.17 Astrophysical and Observational Aspects
20.18 Predictability and Other Cosmic Puzzles
20.19 A Lab for Quantum Gravity–Quantum Stars?
20.20 Concluding Remarks
References
21 Singularities in Cosmological Spacetimes
21.1 Basic Concepts
21.2 Spatially Homogeneous Cosmological Spacetimes
21.3 Spatially Inhomogeneous Cosmologies
21.4 Summary
21.5 Open Questions
References
Part D Confronting Relativity Theories with Observations
22 The Experimental Status of Special and General Relativity
22.1 Introductory Remarks
22.2 Experimental Tests of Special Relativity
22.3 Testing General Relativity
References
23 Observational Constraints on Local Lorentz Invariance
23.1 Spacetime Symmetries in Relativity
23.2 Standard Model Extension
23.3 Experimental Tests of Lorentz Violation
23.4 Summary and Conclusions
References
24 Relativity in GNSS
24.1 The Principle of Equivalence
24.2 Navigation Principles in the GNSS
24.3 Rotation and the Sagnac Effect
24.4 Coordinate Time and TAI
24.5 The Realization of Coordinate Time
24.6 Effects on Satellite Clocks
24.7 Doppler Effect
24.8 Relativity and Orbit Adjustments
24.9 Effects of Earth's Quadrupole Moment
24.10 Secondary Relativistic Effects
24.11 Conclusions
References
25 Quasi-local Black Hole Horizons
25.1 Overview
25.2 Simple Examples
25.3 General Definitions and Results: Trapped Surfaces, Stability and Quasi-local Horizons
25.4 The Equilibrium Case: Isolated Horizons
25.5 Dynamical Horizons
25.6 Outlook
References
26 Gravitational Astronomy
26.1 Background and Motivation
26.2 What Are Gravitational Waves?
26.3 Interaction of Gravitational Waveswith Light and Matter
26.4 Gravitational Wave Detectors
26.5 Gravitational Astronomy
26.6 Conclusions
References
27 Probing Dynamical Spacetimes with Gravitational Waves
27.1 Overview
27.2 Alternative Polarization States
27.3 Probing Gravitational Self-Interaction
27.4 Testing the No Hair Theorem
27.5 Probing the Large-Scale Structure of Spacetime
27.6 Summary
References
Part E General Relativity and the Universe
28 Einstein's Equations, Cosmology, and Astrophysics
28.1 Gravitation Today
28.2 Einstein's Equations
28.3 Cosmology
28.4 Astrophysics
28.5 Conclusion
References
29 Viscous Universe Models
29.1 Viscous Universe Models
29.2 The Standard Model of the Universe
29.3 Viscous Fluid in an Expanding Universe
29.4 Isotropic, Viscous Generalization of the Standard Universe Model
29.5 The Dark Sector of the Universe as a Viscous Fluid
29.6 Viscosity and the AcceleratedExpansion of the Universe
29.7 Viscous Universe Modelswith Variable G and
29.8 Hubble Parameter in the QCD Era of the Early Universe in the Presence of Bulk Viscosity
29.9 Viscous Bianchi Type-I Universe Models
29.10 Viscous Cosmology with Casual Thermodynamics
29.11 Summary
References
30 Friedmann–Lemaître–Robertson–Walker Cosmology
30.1 Motivation
30.2 Dynamical Equations and Simple Solutions
30.3 The Density Parameter
30.4 Cosmological Horizons
30.5 Inhomogeneous Perturbations
30.6 Outlook
References
31 Exact Approach to Inflationary Universe Models
31.1 Aims and Motivations
31.2 Inflation as a Paradigm
31.3 The Exact Solution Approach
31.4 Scalar and Tensor Perturbations
31.5 Hierarchy of Slow-Roll Parameters and Flow Equations
31.6 A Possible Way of Obtaining the Generating Function H()
31.7 Two Interesting Cases
31.8 Conclusion
References
32 Cosmology with the Cosmic Microwave Background
32.1 Contemporary View of our Cosmos
32.2 The Smooth Background Universe
32.3 The Cosmic Microwave Background
32.4 Perturbed Universe: Structure Formation
32.5 CMB Anisotropy and Polarization
32.6 Conclusion
References
Part F Spacetime Beyond Einstein
33 Quantum Gravity
33.1 Why Quantum Gravity?
33.2 Main Approaches to Quantum Gravity
33.3 Outlook
References
34 Quantum Gravity via Causal Dynamical Triangulations
34.1 Asymptotic Safety
34.2 A Lattice Theory for Gravity
34.3 The Phase Diagram
34.4 Relation to Hořava–Lifshitz Gravity
34.5 Conclusions
References
35 String Theory and Primordial Cosmology
35.1 The Standard Big Bang Cosmology
35.2 String Theory
35.3 String Cosmology
35.4 A Higher Dimensional Universe
35.5 Brane Cosmology
35.6 Conclusion
References
36 Quantum Spacetime
36.1 General Ideas for Understanding Quantum Gravity
36.2 Time
36.3 Infinities
36.4 Space
36.5 Quantum Spacetime
References
37 Gravity, Geometry, and the Quantum
37.1 Gravity as a Gauge Theory
37.2 Quantum Geometry
37.3 Quantum Einstein Equations
37.4 Black Holes
37.5 Outlook
References
38 Spin Foams
38.1 Background Ideas
38.2 Spin-Foam Models of Quantum Gravity
38.3 Deriving the Amplitude via a Simpler Theory
38.4 Regge Actionand the Semiclassical Limit
38.5 Two-Point Correlation Functionfrom Spin Foams
38.6 Discussion
References
39 Loop Quantum Cosmology
39.1 Overview
39.2 Quantization of Cosmological Backgrounds
39.3 Inhomogeneous Perturbations in LQC
39.4 LQC Extensionof the Inflationary Scenario
39.5 Conclusions
References
Acknowledgements
About the Authors
Detailed Contents
Index

The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein. Key Topics ́ð Historical origins of the spacetime notion ́ð Basic ideas of special and general relativity ́ð Nature of time and gravity ́ð Mathematical structures ́ð Physical and astrophysical implications ́ð Observational status of the two relativity theories, ́ð Various approaches to unify general relativity and quantum physics. Features ́ð Concise, clear and coherent presentation ́ð Research and application-oriented ́ð Includes recent developments ́ð Exhaustive references to approved data ́ð All chapters with summaries ́ð A resource for graduate students, researchers and teachers in the field

La 4e de couv. indique : "The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein. Key Topics : Historical origins of the spacetime notion, Basic ideas of special and general relativity, Nature of time and gravity, Mathematical structures, Physical and astrophysical implications, Observational status of the two relativity theories, Various approaches to unify general relativity and quantum physics. Features : Concise, clear and coherent presentation, Research and application-oriented, Includes recent developments, Exhaustive references to approved data, All chapters with summaries, A resourse for graduate students, researchers and teachers in the field"

2014-09-26