General Relativity, Cosmology and Astrophysics: Perspectives 100 years after Einstein's stay in Prague

Preface
Contents
Part IGravity and Prague
1 Kepler and Mach\'s Principle
	1 Introduction
	2 Some Important Facts of Planetary Motion
	3 Greek Planetary Astronomy
	4 Copernicus
	5 Kepler
	6 Kepler\'s Significance
	7 Intermezzo: Christian Doppler
	8 Mach and Kinematic Residues in Dynamics
	9 Einstein\'s Reaction to Mach
	10 The Machian Approach: Shape Dynamics
	11 Conclusions
	References
2 Einstein in Prague: Relativity  Then and Now
	1 Introduction
	2 Why and How He was Invited to Prague
	3 Days in Prague
	4 The Czech Culture and Science Responding  to Einstein\'s Work
		4.1 Impact on Czech Physics and Astronomy
	5 Lectures, Seminars and Papers of Albert Einstein in Prague
	6 The Principle of Equivalence
		6.1 Gravitational Redshift Today
	7 Bending of Light
	8 Gravitational Lensing
	9 Prague Works on Gravitation from 1912
		9.1 Intermezzo
		9.2 Dragging of Inertial Frames
		9.3 Relativität and Gravitation. Erwiderungƒ
		9.4 Coda
	References
Part IIClassical General Relativity
3 Observers, Observables and Measurements  in General Relativity
	1 Introduction
	2 Orthogonal Decompositions
	3 Three-Dimensional Notation
	4 Kinematics of the Observer\'s Congruence
	5 Adapted Frames
		5.1 Spatial-Fermi--Walker and Spatial-Lie Temporal  Derivatives
		5.2 Frame Components of the Riemann Tensor
	6 Comparing Families of Observers
	7 Splitting of Derivatives Along a Timelike Curve
		7.1 Projected Absolute Derivative
	8 Preferred Slicing in Spacetimes Admitting  Separable Geodesics
		8.1 Static Spherically Symmetric Spacetimes
	9 Discussion
	References
4 Some Links Between General Relativity  and Other Parts of Physics
	1 Introduction
		1.1 Dynamical Casimir Effect
		1.2 Some Previous Work
	2 Shallow Water Waves
	3 Optics and Maxwell\'s Equations
		3.1 Left-handed Light
		3.2 Zermelo-Randers-Finsler Geometry
		3.3 Invisibility Cloaks
		3.4 Hyperbolic Metamaterials and Two-Time Physics
	4 Chiral Nematics
	5 Gravitational Kinks
		5.1 Bloch Walls
		5.2 Liquid Crystal Droplets
		5.3 Helical Phase
	6 Graphene
		6.1 Cold Atoms
	7 Conclusion and Propects
	References
5 The General Relativistic Two Body Problem  and the Effective One Body Formalism
	1 Introduction
	2 EOB Description of the Conservative Dynamics of Two Body Systems
	3 EOB Description of Radiation Reaction and of the Emitted Waveform During Inspiral
	4 EOB Description of the Merger of Binary Black Holes  and of the Ringdown of the Final Black Hole
	5 EOB Versus NR
		5.1 EOB[NR] Waveforms Versus NR Ones
		5.2 EOB[3PN] Dynamics Versus NR One
	6 Other Developments
		6.1 EOB with Spinning Bodies
		6.2 EOB with Tidally Deformed Bodies
		6.3 EOB and GSF
		6.4 Toward Further Improvements to EOB
	7 Conclusions
	References
6 Gravitational Self-Force: Orbital Mechanics Beyond Geodesic Motion
	1 Background: The Self-Force Domain of the Two-Body  Problem and Astrophysical Relevance
	2 The GSF Program: Foundation
	3 The GSF Program: Computation
		3.1 Mode-Sum Regularization
		3.2 Puncture Method
	4 Orbital Evolution Under the GSF Effect
	5 Gauge Invariant Conservative Effects and Comparison  with Other Methods
	6 Outlook
	References
7 Hamiltonian Formalism for Spinning Black Holes in General Relativity
	1 Introduction
	2 Analytic Representation of Binary Black Holes:  The Brill-Lindquist Initial Value Solution
	3 Spin in Minkowski Space
	4 Spin and Gravity: Asymptotic Flat Spacetimes
		4.1 Hamiltonian for Self-Gravitating Spinning Compact Objects
	5 Post-Newtonian (PN) Hamiltonians
	References
8 Stability of Marginally Outer Trapped  Surfaces and Geometric Inequalities
	1 Introduction
	2 Basics on the Geometry of Spacelike Surfaces
	3 Marginally Outer Trapped Surfaces and Stability
	4 Area-Charge-Topology Inequalities for MOTS
	5 Axially Symmetric MOTS and Angular Momentum
	6 Area-Angular Momentum Inequality for Black Holes
	7 MOTS and Killing Horizons
	8 Further Results and Open Problems
	References
9 Stationary Black-Hole Binaries:  A Non-existence Proof
	1 Introduction
	2 Mathematical Tools
		2.1 Metric and Horizons
		2.2 Field Equations and Linear Problem
	3 Non-existence Proof
		3.1 Integration of the Linear Problem
		3.2 Ernst Potential on the Axis
		3.3 Weyl-Bach Force Between the Black Holes
		3.4 Angular Momentum-Area Inequality and Non-existence Proof
	4 Summary
	5 Supplement
		5.1 Degenerate Horizons
		5.2 Further Applications of the Inverse Method
	References
10 Dynamic and Thermodynamic Stability  of Black Holes and Black Branes
	1 Introduction
	2 Dynamic and Thermodynamic Stability of Black  Holes and Black Branes
	References
11 Instability of Anti-de Sitter Spacetime
	1 Introduction
	2 Instability of Anti-de Sitter Spacetime
	References
12 Higher-Dimensional Black Holes
	1 Introduction
	2 Black Holes in Kaluza-Klein Theory
	3 Asymptotically Flat Black Holes
		3.1 Introduction
		3.2 Myers-Perry Black Holes
		3.3 Black Rings
		3.4 Black Saturn and Generalizations
		3.5 Classification of Asymptotically Flat Black Holes
		3.6 Perturbative Solutions
	References
13 Black Holes, Hidden Symmetry and Complete Integrability: Brief Review
	1 Introduction
	2 Four Dimensional Kerr-NUT-ADS Metric and Its Higher Dimensional Generalization
		2.1 Four Dimensional Kerr-NUT-ADS Spacetime
		2.2 Higher Dimensional Solutions
	3 Principal Conformal Killing-Yano Tensor
		3.1 Definition
		3.2 Remarkable Properties of PCKYT
	4 Complete Integrability
		4.1 Liouville Theorem
		4.2 Relativistic Particle as Dynamical System
		4.3 Page\'s Proposal
	5 PCKYT and Killing-Yano Tower
		5.1 Killing-Yano Tensors
		5.2 Killing-Yano Tower
	6 Separation of Variables
		6.1 General Remarks
		6.2 Complete Separation of Variables in Kerr-NUT-ADS Spacetime
		6.3 Complete Integrability and Separation of Variables in Weakly Charged Black Holes
	References
Part IIICosmology and Quantum Gravity
14 Cosmological Models and Stability
	1 Introduction
		1.1 The Cosmological Principle
	2 Cosmological Models
		2.1 Cosmological Problems
	3 Asymptotics of Cosmological Models
	4 Results on Nonlinear Stability
		4.1 Minkowski
		4.2 de Sitter
		4.3 Milne
	5 Generalized Kasner Spacetimes
		5.1 From α to ω
	6 Concluding Remarks
	References
15 Inflation and Birth of Cosmological Perturbations
	1 Introduction
		1.1 Horizon Problem
		1.2 Flatness Problem
		1.3 Inflation as a Solution to Horizon and Flatness Problems
	2 Slow-Roll Inflation and Vacuum Fluctuations
		2.1 Curvature Perturbation
		2.2 Tensor Perturbation
	3 Origin of Non-Gaussianity
		3.1 Non-Gaussianity From Self-Interaction/Non-Trivial Vacuum
		3.2 Non-Gaussianity From Multi-Field Dynamics
	4 δN Formalism
	5 Summary
	References
16 Loop Quantum Gravity and the Planck  Regime of Cosmology
	1 Introduction
	2 Setting the Stage
	3 Why Pre-inflationary Dynamics Matters
	4 The LQG Strategy
	5 Analytical Aspects
	6 Numerical Aspects, Observations and Self-Consistency
		6.1 WMAP Phenomenology
		6.2 Evolution of the Background
		6.3 Evolution of Perturbations
		6.4 Self Consistency
	7 Summary and Discussion
	References
17 The Inflationary Origin of the Seeds of Cosmic Structure: Quantum Theory and the Need for Novel Physics
	1 Introduction
	2 The General Setting
	3 The Stern-Gerlach Analogy
	4 A Word About Collapse Theories
	5 The Self Consistent Semiclassical Configurations
	6 Collapse
	7 Relation to Other Approaches
	8 Application to Inflation
		8.1 The Homogeneous and Isotropic Case: SSC I
		8.2 A Simple Inhomogeneous and Anisotropic Case: SSC II
		8.3 The Collapse: Joining SSC-I and SSC-II
	9 Phenomenological Studies
		9.1 Analysis of the Phenomenology
	10 Conclusions
	References
18 Quantum Gravity: The View From Particle Physics
	1 Introduction
	2 The Divergence Problem
	3 The Role of Matter
	4 The Hierarchy Problem
	5 From the Standard Model to the Planck Scale
	6 Anomalies
	7 Outlook
	References
Part IVNumerical Relativity and RelativisticAstrophysics
19 Three Little Pieces for Computer  and Relativity
	1 Introduction
	2 First Piece: From Neutrons Star to Gamma-Ray Bursts
		2.1 The Numerical Setup
		2.2 The Basic Dynamics
		2.3 Comparison with Observations
		2.4 Summary
	3 Second Piece: A Dynamical Hoop Conjecture
		3.1 The Numerical Setup
		3.2 The Basic Dynamics
		3.3 Critical Behaviour and Scaling
		3.4 Summary
	4 Third Piece: Horizons as Probes of Black-Hole Dynamics
		4.1 The Basic Picture
		4.2 A Useful Playground
		4.3 A More General View
		4.4 Summary
	5 Conclusions
	References
20 Instabilities of Relativistic Stars
	1 Introduction
	2 Action and Canonical Energy
	3 Local Stability
		3.1 Convective Instability
		3.2 Convective Instability due to Differential Rotation:  The Solberg Criterion
	4 Axisymmetric Instability and Turning Points
		4.1 Turning Point Instability
	5 Nonaxisymmetric Instabilities
	References
21 Gravity Talks: Observing the Universe  with Gravitational Waves
	1 Introduction
	2 Light Deflection and Gravitational Wave Detection
	3 The Global Interferometer Network
	4 Data Analysis
	5 Observables
	6 Gravitational Waves from Neutron Stars and Black Holes
		6.1 Neutron Star Binary Coalescence
		6.2 Neutron Star Interiors
		6.3 Black Hole Binary Coalescence
		6.4 Gravitational Wave Pulsars
	7 Other Gravitational Wave Sources
	8 Detecting Gravitational Waves from Space
		8.1 LISA and eLISA
		8.2 LISA Science
	9 Conclusion
	References
22 LISA in 2012 and Beyond: 20 Years After  the First Proposal
	1 Introduction
	2 Planned ESA Cosmic Vision L1 Selection in 2011
	3 The eLISA/NGO Mission Concept
	4 The eLISA Consortium
	5 The ESA L1 Decision and Its Aftermath
	6 Naming the Mission Concepts
	7 Conclusion
	References
23 Einstein\'s Gravity as Seen by a Cosmic Lighthouse Keeper
	1 Introduction
		1.1 Pulsars
		1.2 Pulsars and Their Companions
		1.3 Nature is Kind...
		1.4 Precision Experiments
	2 The Hulse-Taylor Pulsar: Gravitational Wave Damping
	3 The Double Pulsar
	4 Relativistic Spin-Orbit Coupling
	5 Alternative Theories
	6 Detecting Gravitational Waves with Pulsars
	7 The Future and the Ultimate Laboratory
	8 Summary and Conclusions
	References
24 The Astrophysical Signatures of Black Holes: The Horizon, The ISCO, The Ergosphere  and The Light Circle
	1 Introduction
	2 The Kerr Metric and Its Symmetries
	3 The Horizon
	4 The Ergosphere
		4.1 The Penrose Process
		4.2 The Blandford-Znajek Mechanism
	5 The ISCO
		5.1 ISCO for Keplerian, Circular Orbits (Circular Geodesics)
		5.2 The Shakura--Sunyaev ISCO Paradigm for Thin  Accretion Disks
		5.3 Leaving the ISCO
		5.4 Evidence for ISCO from the Observed Variability
	6 The Light Circle
	7 Conclusions
	References
25 Energy Extraction from Spinning Black Holes Via Relativistic Jets
	1 Introduction
	2 Computer Simulations of Black Hole Accretion and Jets
	3 Empirical Evidence for the Generalized Penrose Process
		3.1 Spin Parameters of Stellar-Mass Black Holes
		3.2 Correlation Between Black Hole Spin and Jet Radio Power
		3.3 Why Generalized Penrose Process?
	4 Summary
	References