Whiting / Spallicci / Blanchet Mass and Motion in General Relativity

1. Auflage 2011
ISBN: 978-90-481-3015-3
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 626 Seiten

From the infinitesimal scale of particle physics to the cosmic scale of the universe, research is concerned with the nature of mass. While there have been spectacular advances in physics during the past century, mass still remains a mysterious entity at the forefront of current research. Our current perspective on gravitation has arisen over millennia, through the contemplation of falling apples, lift thought experiments and notions of stars spiraling into black holes.  In this volume, the world's leading scientists offer a multifaceted approach to mass by giving a concise and introductory presentation based on insights from their respective fields of research on gravity. The main theme is mass and its motion within general relativity and other theories of gravity, particularly for compact bodies. Within this framework, all articles are tied together coherently, covering post-Newtonian and related methods as well as the self-force approach to the analysis of motion in curved space-time, closing with an overview of the historical development and a snapshot on the actual state of the art. All contributions reflect the fundamental role of mass in physics, from issues related to Newton's laws, to the effect of self-force and radiation reaction within theories of gravitation, to the role of the Higgs boson in modern physics. High-precision measurements are described in detail, modified theories of gravity reproducing experimental data are investigated as alternatives to dark matter, and the fundamental problem of reconciling any theory of gravity with the physics of quantum fields is addressed. Auxiliary chapters set the framework for theoretical contributions within the broader context of experimental physics. The book is based upon the lectures of the CNRS School on Mass held in Orléans, France, in June 2008. All contributions have been anonymously refereed and, with the cooperation of the authors, revised by the editors to ensure overall consistency.

Autoren/Hrsg.

Whiting, Bernhard

Spallicci, Alessandro

Blanchet, Luc

Whiting, Bernard

Inhaltsverzeichnis

1;Mass and Motion in General Relativity;1
1.1;Mass and Motion in General Relativity;5
1.2;Contents;9
1.3;The Higgs Mechanism and the Origin of Mass;19
1.3.1;1 The Standard Model and the Generation of Particle Masses;19
1.3.1.1;1.1 The Elementary Particles and Their Interactions;20
1.3.1.2;1.2 The Standard Model of Particle Physics;21
1.3.1.3;1.3 The Higgs Mechanism for Mass Generation;23
1.3.2;2 The Profile of the Higgs Particle;26
1.3.2.1;2.1 Characteristics of the Higgs Boson;26
1.3.2.2;2.2 Constraints on the Higgs Boson Mass;27
1.3.2.3;2.3 The Higgs Decay Modes and Their Rates;29
1.3.3;3 Higgs Production at the LHC;31
1.3.3.1;3.1 The Large Hadron Collider;31
1.3.3.2;3.2 The Production of the Higgs Boson;32
1.3.3.3;3.3 Detection of the Higgs Boson;33
1.3.3.4;3.4 Determination of the Higgs Boson Properties;36
1.3.4;4 The Higgs Beyond the Standard Model;38
1.3.5;5 Conclusions;40
1.3.6;References;41
1.4;Testing Basic Laws of Gravitation – Are Our Postulates on Dynamics and Gravitation Supported by Experimental Evidence?;42
1.4.1;1 Introduction – Why Gravity Is So Exceptional;42
1.4.2;2 Key Features of Gravity;44
1.4.3;3 Standard Tests of the Foundations of Special and General Relativity;45
1.4.3.1;3.1 Tests of Special Relativity;45
1.4.3.1.1;3.1.1 The Constancy of the Speed of Light;45
1.4.3.1.2;3.1.2 The Relativity Principle;46
1.4.3.1.3;3.1.3 The Consequence;47
1.4.3.2;3.2 Tests of the Universality of Free Fall;47
1.4.3.3;3.3 Tests of the Universality of the Gravitational Redshift;48
1.4.3.4;3.4 The Consequence;49
1.4.4;4 Tests of Predictions;51
1.4.4.1;4.1 The Gravitational Redshift;52
1.4.4.2;4.2 Light Deflection;53
1.4.4.3;4.3 Perihelion/Periastron Shift;54
1.4.4.4;4.4 Gravitational Time Delay;55
1.4.4.4.1;4.4.1 Direct Measurement;55
1.4.4.4.2;4.4.2 Measurement of Frequency Change;55
1.4.4.4.3;4.4.3 Remarks;57
1.4.4.5;4.5 Lense–Thirring Effect;57
1.4.4.6;4.6 Schiff Effect;58
1.4.4.7;4.7 The Strong Equivalence Principle;58
1.4.5;5 Why New Tests?;59
1.4.5.1;5.1 Dark Clouds – Problems with GR;59
1.4.5.1.1;5.1.1 Dark Matter;59
1.4.5.1.2;5.1.2 Dark Energy;60
1.4.5.1.3;5.1.3 Pioneer Anomaly;60
1.4.5.1.4;5.1.4 Flyby Anomaly;61
1.4.5.1.5;5.1.5 Increase of Astronomical Unit;61
1.4.5.1.6;5.1.6 Quadrupole and Octupole Anomaly;62
1.4.5.2;5.2 The Search for Quantum Gravity;62
1.4.5.3;5.3 Possible New Effects;62
1.4.6;6 How to Search for ``New Physics'';63
1.4.6.1;6.1 Better Accuracy and Sensitivity;63
1.4.6.2;6.2 Extreme Situations;64
1.4.6.2.1;6.2.1 Extreme High Energy;64
1.4.6.2.2;6.2.2 Extreme Low Energy;64
1.4.6.2.3;6.2.3 Large Distances;65
1.4.6.2.4;6.2.4 Small Accelerations;65
1.4.6.2.5;6.2.5 Large Accelerations;65
1.4.6.2.6;6.2.6 Strong Gravitational Fields;65
1.4.6.3;6.3 Investigation of ``Exotic'' Issues;66
1.4.7;7 Testing ``Exotic'' but Fundamental Issues;67
1.4.7.1;7.1 Active and Passive Mass;67
1.4.7.2;7.2 Active and Passive Charge;68
1.4.7.3;7.3 Active and Passive Magnetic Moment;69
1.4.7.4;7.4 Charge Conservation;69
1.4.7.5;7.5 Small Accelerations;70
1.4.7.6;7.6 Test of the Inertial Law;71
1.4.7.6.1;7.6.1 Higher Order Equation of Motion for Classical Particles;72
1.4.7.6.2;7.6.2 Higher Order Equation of Motion for Quantum Particles;73
1.4.7.7;7.7 Can Gravity Be Transformed Away?;74
1.4.7.7.1;7.7.1 Finsler Geometry;74
1.4.7.7.2;7.7.2 Testing Finslerian Anisotropy in Tangent Space;75
1.4.7.7.3;7.7.3 Finslerian Geodesic Equation;75
1.4.8;8 Summary;77
1.4.9;References;77
1.5;Mass Metrology and the International System of Units (SI);83
1.5.1;1 Introduction;83
1.5.2;2 The SI;84
1.5.2.1;2.1 Base Units/Base Quantities;84
1.5.2.2;2.2 Gaussian Units;86
1.5.2.3;2.3 Planck Units, Natural Units, and Atomic Units;87
1.5.3;3 Practical Reasons for Redefining the Kilogram;87
1.5.3.1;3.1 Internal Evidence Among 1 kg Artifact Mass Standards;87
1.5.3.2;3.2 Fundamental Constants;89
1.5.3.3;3.3 Electrical Metrology;91
1.5.3.4;3.4 Relative Atomic Masses;93
1.5.4;4 Routes to a New Kilogram;94
1.5.5;5 Realizing a New Kilogram Definition in Practice;95
1.5.5.1;5.1 Watt Balances;96
1.5.5.2;5.2 Silicon X-Ray Crystal Density (XRCD);97
1.5.5.3;5.3 Experimental Results;98
1.5.6;6 Proposals for a New SI;99
1.5.6.1;6.1 Consensus Building and Formal Approval;99
1.5.6.2;6.2 An SI Based on Defined Values of a Set of Constants;100
1.5.7;7 Conclusion;100
1.5.8;References;101
1.6;Mass and Angular Momentum in General Relativity;103
1.6.1;1 Issues Around the Notion of Gravitational Energy in General Relativity;104
1.6.1.1;1.1 Energy–Momentum Density for Matter Fields;104
1.6.1.2;1.2 Problems when Defining a Gravitational Energy–Momentum;106
1.6.1.2.1;1.2.1 Nonlocal Character of the Gravitational Energy;107
1.6.1.3;1.3 Notation;108
1.6.1.3.1;1.3.1 3+1 Decompositions;108
1.6.1.3.2;1.3.2 Closed 2-Surfaces;109
1.6.2;2 Spacetimes with Killing Vectors: Komar Quantities;110
1.6.2.1;2.1 Komar Mass;110
1.6.2.2;2.2 Komar Angular Momentum;111
1.6.3;3 Total Mass of Isolated Systems in General Relativity;111
1.6.3.1;3.1 Asymptotic Flatness Characterization of Isolated Systems;111
1.6.3.2;3.2 Asymptotic Euclidean Slices;112
1.6.3.2.1;3.2.1 Asymptotic Symmetries at Spatial Infinity;113
1.6.3.3;3.3 ADM Quantities;113
1.6.3.3.1;3.3.1 ADM Energy;115
1.6.3.3.2;3.3.2 ADM 4-Momentum and ADM Mass;118
1.6.3.3.3;3.3.3 ADM Angular Momentum;120
1.6.3.4;3.4 Bondi Energy and Linear Momentum;121
1.6.3.4.1;3.4.1 Null Infinity;122
1.6.3.4.2;3.4.2 Symmetries at Null Infinity;122
1.6.3.4.3;3.4.3 Bondi–Sachs 4-Momentum;123
1.6.4;4 Notions of Mass for Bounded Regions: Quasi-Local Masses;124
1.6.4.1;4.1 Ingredients in the Quasi-Local Constructions;124
1.6.4.2;4.2 Some Relevant Quasi-Local Masses;125
1.6.4.2.1;4.2.1 Round Spheres: Misner–Sharp Energy;125
1.6.4.2.2;4.2.2 Brown–York Energy;125
1.6.4.2.3;4.2.3 Hawking, Geroch, and Hayward Energies;127
1.6.4.2.4;4.2.4 Bartnik Mass;129
1.6.4.3;4.3 Some Remarks on Quasi-Local Angular Momentum;130
1.6.4.4;4.4 A Study Case: Quasi-Local Mass of Black Hole IHs;131
1.6.4.4.1;4.4.1 A Brief Review of IHs;131
1.6.4.4.2;4.4.2 An Overview of the Hamiltonian Analysis of IHs;132
1.6.5;5 Global and Quasi-Local Quantities in Black Hole Physics;134
1.6.5.1;5.1 Penrose Inequality: a Claim for an Improved Mass Positivity Result for Black Holes;135
1.6.5.2;5.2 Black Hole (Thermo-)dynamics;135
1.6.5.3;5.3 Black Hole Extremality: a Mass–Angular Momentum Inequality;137
1.6.6;6 Conclusions;137
1.6.7;References;139
1.7;Post-Newtonian Theory and the Two-Body Problem;141
1.7.1;1 Introduction;141
1.7.2;2 Post-Newtonian Formalism;144
1.7.2.1;2.1 Einstein Field Equations;144
1.7.2.2;2.2 Post-Newtonian Iteration in the Near Zone;147
1.7.2.3;2.3 Post-Newtonian Expansion Calculated by Matching;151
1.7.2.4;2.4 Multipole Moments of a Post-Newtonian Source;155
1.7.2.5;2.5 Radiation Field and Polarization Waveforms;159
1.7.2.6;2.6 Radiative Moments Versus Source Moments;161
1.7.3;3 Inspiralling Compact Binaries;163
1.7.3.1;3.1 Stress–Energy Tensor of Spinning Particles;163
1.7.3.2;3.2 Hadamard Regularization;166
1.7.3.3;3.3 Dimensional Regularization;169
1.7.3.4;3.4 Energy and Flux of Compact Binaries;172
1.7.3.5;3.5 Waveform of Compact Binaries;176
1.7.3.6;3.6 Spin–Orbit Contributions in the Energy and Flux;178
1.7.4;References;180
1.8;Post-Newtonian Methods: Analytic Results on the Binary Problem;183
1.8.1;1 Introduction;183
1.8.2;2 Systems in Newtonian Gravity in Canonical Form;185
1.8.3;3 Canonical General Relativity and PN Expansions;187
1.8.3.1;3.1 Canonical Variables of the Gravitational Field ;189
1.8.3.2;3.2 Brill–Lindquist Initial-Value Solution for Binary Black Holes;191
1.8.3.3;3.3 Skeleton Hamiltonian;192
1.8.3.4;3.4 Functional Representation of Compact Objects;195
1.8.3.5;3.5 PN Expansion of the Routh Functional;201
1.8.3.6;3.6 Near-Zone Energy Loss Versus Far-Zone Energy Flux;201
1.8.4;4 Binary Point Masses to Higher PN Order;203
1.8.4.1;4.1 Conservative Hamiltonians;203
1.8.4.2;4.2 Dynamical Invariants;204
1.8.4.3;4.3 ISCO and the PN Framework;206
1.8.4.4;4.4 PN Dissipative Binary Dynamics;208
1.8.5;5 Toward Binary Spinning Black Holes;208
1.8.5.1;5.1 Approximate Hamiltonians for Spinning Binaries;212
1.8.6;6 Lorentz-Covariant Approach and PN Expansions;216
1.8.6.1;6.1 PM and PN Expansions;218
1.8.6.2;6.2 PN Expansion in the Near Zone;219
1.8.6.3;6.3 PN Expansion in the Far Zone;221
1.8.7;7 Energy Loss and Gravitational Wave Emission;222
1.8.7.1;7.1 Orbital Decay to 4 PN Order;222
1.8.7.2;7.2 Gravitational Waveform to 1.5 PN Order;223
1.8.8;References;225
1.9;The Effective One-Body Description of the Two-Body Problem;227
1.9.1;1 Introduction;227
1.9.2;2 Motion and Radiation of Binary Black Holes: PN Expanded Results;229
1.9.3;3 Conservative Dynamics of Binary Black Holes: the EOB Approach;231
1.9.4;4 Description of Radiation–Reaction Effects in the EOB Approach;240
1.9.4.1;4.1 Resummation of Taylor Using a One-Parameter Family of Padé Approximants: Tuning vpole;243
1.9.4.2;4.2 Parameter-Free Resummation of Waveform and Energy Flux;246
1.9.5;5 EOB Dynamics and Waveforms;254
1.9.5.1;5.1 Post–Post-Circular Initial Data;254
1.9.5.2;5.2 EOB Waveforms;255
1.9.5.3;5.3 EOB Dynamics;257
1.9.6;6 EOB and NR Waveforms;259
1.9.7;7 Conclusions;264
1.9.8;References;265
1.10;Introduction to Gravitational Self-Force;269
1.10.1;1 Motion of Bodies in General Relativity;269
1.10.2;2 Point Particles in General Relativity;270
1.10.3;3 Point Particles in Linearized Gravity;271
1.10.4;4 Lorenz Gauge Relaxation;272
1.10.5;5 Hadamard Expansions;272
1.10.5.1;5.1 Hadamard Expansions for a Point Particle Source;274
1.10.6;6 Equations of Motion Including Self-Force;275
1.10.6.1;6.1 The MiSaTaQuWa Equations;275
1.10.6.2;6.2 The Detweiler–Whiting Reformulation;276
1.10.7;7 How Should Gravitational Self-Force Be Derived?;277
1.10.8;References;278
1.11;Derivation of Gravitational Self-Force;279
1.11.1;1 Difficulties with Usual Derivations;279
1.11.2;2 Rigorous Derivation Requirements;280
1.11.3;3 Limits of Spacetimes;280
1.11.4;4 Our Basic Assumptions;281
1.11.4.1;4.1 Additional Uniformity Requirement;281
1.11.5;5 Geodesic Motion;282
1.11.6;6 Corrections to Motion;283
1.11.6.1;6.1 Calculation of the Perturbed Motion;284
1.11.7;7 Interpretation of Results;285
1.11.8;8 Self-Consistent Equations;285
1.11.9;9 Summary;286
1.11.10;References;286
1.12;Elementary Development of the Gravitational Self-Force;287
1.12.1;1 Introduction;287
1.12.1.1;1.1 Outline;289
1.12.1.2;1.2 Notation;290
1.12.2;2 Newtonian Examples of Self-Force and Gauge Issues;291
1.12.3;3 Classical Electromagnetic Self-Force;293
1.12.4;4 A Toy Problem with Two Length Scales That Creates a Challenge for Numerical Analysis;294
1.12.4.1;4.1 An Approach Which Avoids the Small Length Scale;295
1.12.4.2;4.2 An Alternative That Resolves Boundary Condition Issues;297
1.12.5;5 Perturbation Theory;298
1.12.5.1;5.1 Standard Perturbation Theory in General Relativity;299
1.12.5.2;5.2 An Application of Perturbation Theory: Locally Inertial Coordinates;301
1.12.5.3;5.3 Metric Perturbations in the Neighborhood of a Point Mass;303
1.12.5.4;5.4 A Small Object Moving Through Spacetime;305
1.12.6;6 Self-Force from Gravitational Perturbation Theory;307
1.12.6.1;6.1 Dissipative and Conservative Parts;308
1.12.6.2;6.2 Gravitational Self-Force Implementations;309
1.12.6.2.1;6.2.1 Field Regularization Via the Effective Source;309
1.12.6.2.2;6.2.2 Mode-Sum Regularization;310
1.12.6.2.3;6.2.3 The Gravitational Self-Force Actually Resulting in Acceleration;310
1.12.7;7 Perturbative Gauge Transformations;311
1.12.8;8 Gauge Confusion and the Gravitational Self-Force;313
1.12.9;9 Steps in the Analysis of the Gravitational Self-Force;314
1.12.10;10 Applications;316
1.12.10.1;10.1 Gravitational Self-Force Effects on Circular Orbits of the Schwarzschild Geometry;316
1.12.10.2;10.2 Field Regularization Via the Effective Source;317
1.12.11;11 Concluding Remarks;320
1.12.12;References;322
1.13;Constructing the Self-Force;324
1.13.1;1 Introduction;324
1.13.2;2 Geometric Elements;326
1.13.3;3 Coordinate Systems;327
1.13.4;4 Field Equation and Particle Motion;331
1.13.5;5 Retarded Green's Function;331
1.13.6;6 Alternate Green's Function;333
1.13.7;7 Fields Near the World Line;334
1.13.8;8 Self-Force;336
1.13.9;9 Axiomatic Approach;337
1.13.10;10 Conclusion;339
1.13.11;References;340
1.14;Computational Methods for the Self-Force in Black Hole Spacetimes;341
1.14.1;1 Introduction and Overview;341
1.14.1.1;1.1 The MiSaTaQuWa Formula;343
1.14.1.2;1.2 Gauge Dependence;344
1.14.1.3;1.3 Implementation Strategies;345
1.14.1.3.1;1.3.1 Quasi-Local Calculations;346
1.14.1.3.2;1.3.2 Weak-Field Analysis;346
1.14.1.3.3;1.3.3 Radiation-Gauge Regularization;346
1.14.1.3.4;1.3.4 Mode-Sum Method;346
1.14.1.3.5;1.3.5 ``Puncture'' Methods;347
1.14.2;2 Mode-Sum Method;349
1.14.2.1;2.1 An Elementary Example;350
1.14.2.2;2.2 The Mode-Sum Formula;352
1.14.2.3;2.3 Derivation of the Regularization Parameters;353
1.14.3;3 Numerical Implementation Strategies;357
1.14.3.1;3.1 Overcoming the Gauge Problem;358
1.14.3.1.1;3.1.1 Self-Force in an ``Hybrid'' Gauge;358
1.14.3.1.2;3.1.2 Generalized SF and Gauge Invariants;359
1.14.3.1.3;3.1.3 Radiation-Gauge Regularization;360
1.14.3.1.4;3.1.4 Direct Lorenz-Gauge Implementation;360
1.14.3.2;3.2 Numerical Representation of the Point Particle;361
1.14.3.2.1;3.2.1 Particle Representation in the Time Domain;361
1.14.3.2.2;3.2.2 Particle Representation in the Frequency Domain: the High-Frequency Problem and Its Resolution;364
1.14.4;4 An Example: Gravitational Self-Force in Schwarzschild Via 1+1D Evolution in Lorenz Gauge;366
1.14.4.1;4.1 Lorenz-Gauge Formulation;366
1.14.4.2;4.2 Numerical Implementation;368
1.14.5;5 Toward Self-Force Calculations in Kerr: the Puncture Method and m-Mode Regularization;370
1.14.5.1;5.1 Puncture Method in 2+1D;370
1.14.5.2;5.2 m-Mode Regularization;372
1.14.6;6 Reflections and Prospects;374
1.14.7;References;378
1.15;Radiation Reaction and Energy–Momentum Conservation;381
1.15.1;1 Introduction;381
1.15.2;2 Energy–Momentum Balance Equation;383
1.15.2.1;2.1 Decomposition of the Stress Tensor;385
1.15.2.2;2.2 Bound Momentum;388
1.15.2.3;2.3 The Rest Frame (Nonrelativistic Limit);391
1.15.3;3 Flat Dimensions Other than Four;392
1.15.4;4 Local Method for Curved Space-Time;393
1.15.4.1;4.1 Hadamard Expansion in Any Dimensions;394
1.15.4.2;4.2 Divergences;395
1.15.4.3;4.3 Four Dimensions;398
1.15.4.4;4.4 Self and Radiative Forces in Curved Space-Time;400
1.15.5;5 Gravitational Radiation;401
1.15.5.1;5.1 Bianchi Identity;401
1.15.5.2;5.2 Vacuum Background;403
1.15.5.3;5.3 Gravitational Radiation for Non-Geodesic Motion;404
1.15.6;6 Conclusions;405
1.15.7;References;406
1.16;The State of Current Self-Force Research;408
1.16.1;1 Introduction;408
1.16.2;2 The Teukolsky Equation;410
1.16.2.1;2.1 The Inhomogeneous Teukolsky Equation with a Distributional Source;410
1.16.2.2;2.2 Adiabatic Waveforms;411
1.16.2.3;2.3 Numerical Solution of the Teukolsky Equation;412
1.16.2.4;2.4 The Linearized Einstein Equations;413
1.16.3;3 Frequency-Domain Calculations of the Self-Force;414
1.16.3.1;3.1 Mode-Sum Regularization;414
1.16.3.2;3.2 The Detweiler–Whiting Regular Part of the Self-Force;415
1.16.4;4 Time-Domain Calculations of the Self-Force;416
1.16.4.1;4.1 1+1D Numerical Simulations;416
1.16.4.2;4.2 2+1D Numerical Simulations;417
1.16.4.2.1;4.2.1 m-Mode Regularization;418
1.16.4.2.2;4.2.2 The Square of the Geodesic Distance;419
1.16.4.2.3;4.2.3 The Puncture Function;420
1.16.5;5 Post-adiabatic Self-Force-Driven Orbital Evolution;421
1.16.5.1;5.1 The Importance of Second-Order Self-Forces;421
1.16.5.2;5.2 Conservative Self-Force Effects;425
1.16.6;References;426
1.17;High-Accuracy Comparison Between the Post-Newtonianand Self-Force Dynamics of Black-Hole Binaries;428
1.17.1;1 Introduction and Motivation;429
1.17.2;2 The Gauge-Invariant Redshift Observable;431
1.17.3;3 Regularization Issues in the SF and PN Formalisms;432
1.17.4;4 Circular Orbits in the Perturbed Schwarzschild Geometry;434
1.17.5;5 Overview of the 3PN Calculation;436
1.17.5.1;5.1 Iterative PN Computation of the Metric;436
1.17.5.2;5.2 The Example of the Zeroth-Order Iteration;439
1.17.6;6 Logarithmic Terms at 4PN and 5PN Orders;440
1.17.6.1;6.1 Physical Origin of Logarithmic Terms;440
1.17.6.2;6.2 Expression of the Near-Zone Metric;442
1.17.7;7 Post-Newtonian Results for the Redshift Observable;443
1.17.8;8 Numerical Evaluation of Post-Newtonian Coefficients;446
1.17.8.1;8.1 Overview;447
1.17.8.2;8.2 Framework for Evaluating PN Coefficients Numerically;448
1.17.8.3;8.3 Consistency Between Analytically and Numerically Determined PN Coefficients;450
1.17.8.4;8.4 Determining Higher Order PN Terms Numerically;451
1.17.8.5;8.5 Summary;452
1.17.9;References;454
1.18;LISA and Capture Sources;456
1.18.1;1 LISA – A Mission to Detect and Observe Gravitational Waves;456
1.18.1.1;1.1 Mission Concept;457
1.18.1.2;1.2 Sensitivity;458
1.18.1.3;1.3 Measurement Principle;459
1.18.2;2 Capture Sources;461
1.18.3;3 Science Return;462
1.18.4;4 Detection;464
1.18.4.1;4.1 Capture Rates;464
1.18.4.2;4.2 Signal Characteristics;465
1.18.4.3;4.3 Data Analysis;467
1.18.5;5 Summary and Conclusions;469
1.18.6;References;470
1.19;Motion in Alternative Theories of Gravity;473
1.19.1;1 Introduction;473
1.19.2;2 Modifying the Matter Action;474
1.19.3;3 Modified Motion in Metric Theories?;476
1.19.4;4 Scalar-Tensor Theories of Gravity;480
1.19.4.1;4.1 Weak-Field Predictions;481
1.19.4.2;4.2 Strong-Field Predictions;483
1.19.4.3;4.3 Binary-Pulsar Tests;484
1.19.4.4;4.4 Black Holes in Scalar-Tensor Gravity;488
1.19.5;5 Extended Bodies;489
1.19.6;6 Modified Newtonian Dynamics;491
1.19.6.1;6.1 Mass-Dependent Models?;492
1.19.6.2;6.2 Aquadratic Lagrangians or k-Essence;493
1.19.6.3;6.3 Difficulties;494
1.19.6.4;6.4 Nonminimal Couplings;497
1.19.7;7 Conclusions;498
1.19.8;References;499
1.20;Mass, Inertia, and Gravitation;502
1.20.1;1 Introduction;502
1.20.2;2 Vacuum Fluctuations and Inertia;505
1.20.2.1;2.1 Linear Response Formalism;505
1.20.2.2;2.2 Response to Motions;509
1.20.2.3;2.3 Relativity of Motion;513
1.20.2.4;2.4 Inertia of Vacuum Fields;515
1.20.3;3 Mass as a Quantum Observable;519
1.20.3.1;3.1 Quantum Fluctuations of Mass;519
1.20.3.2;3.2 Mass and Conformal Symmetries;521
1.20.4;4 Metric Extensions of GR;525
1.20.4.1;4.1 Radiative Corrections;526
1.20.4.2;4.2 Anomalous Curvatures;529
1.20.4.3;4.3 Phenomenology in the Solar System;531
1.20.5;5 Conclusion;537
1.20.6;References;538
1.21;Motion in Quantum Gravity;542
1.21.1;1 Introduction;542
1.21.1.1;1.1 The Problem of Defining Motion in Quantum Gravity;542
1.21.1.2;1.2 Quantum Gravity;543
1.21.1.3;1.3 Three-Dimensional Quantum Gravity Is a Fruitful Toy Model;545
1.21.1.4;1.4 Outline of the Article;546
1.21.2;2 Casting an Eye Over Loop Quantum Gravity;547
1.21.2.1;2.1 The Classical Theory: Main Ingredients;547
1.21.2.2;2.2 The Route to the Quantization of Gravity;549
1.21.2.3;2.3 Spin-Networks Are States of Quantum Geometry;550
1.21.2.4;2.4 The Problem of the Hamiltonian Constraint;552
1.21.3;3 Three-Dimensional Euclidean Quantum Gravity;553
1.21.3.1;3.1 Construction of the Noncommutative Space;554
1.21.3.1.1;3.1.1 Quantum Gravity and Noncommutativity;554
1.21.3.1.2;3.1.2 The Quantum Double Plays the Role of the Isometry Algebra;555
1.21.3.1.3;3.1.3 The Quantum Geometry Defined by Its Momenta Space;556
1.21.3.1.4;3.1.4 The Fuzzy Space Formulation;557
1.21.3.1.5;3.1.5 Relation to the Classical Geometry;558
1.21.3.2;3.2 Constructing the Quantum Dynamics;561
1.21.3.2.1;3.2.1 An Integral on the Quantum Space to Define the Action;561
1.21.3.2.2;3.2.2 Derivative Operators to Define the Dynamics;561
1.21.3.2.3;3.2.3 Free Field: Solutions and Properties;562
1.21.3.3;3.3 Particles Evolving in the Fuzzy Space;563
1.21.3.4;3.4 Reduction to One Dimension;564
1.21.3.4.1;3.4.1 Dynamics of a Particle: Linear versus Nonlinear;566
1.21.3.4.2;3.4.2 Background Independent Motion;568
1.21.4;4 Discussion;569
1.21.5;References;570
1.22;Free Fall and Self-Force: an Historical Perspective;571
1.22.1;1 Introduction;572
1.22.2;2 The Historical Heritage;573
1.22.3;3 Uniqueness of Acceleration and the Newtonian Back-Action;575
1.22.4;4 The Controversy on the Repulsion and on the Particle Velocity at the Horizon;579
1.22.5;5 Black Hole Perturbations;584
1.22.6;6 Numerical Solution;588
1.22.7;7 Relativistic Radial Fall Affected by the Falling Mass;592
1.22.7.1;7.1 The Self-Force;592
1.22.7.2;7.2 The Pragmatic Approach;597
1.22.8;8 The State of the Art;600
1.22.8.1;8.1 Trajectory;601
1.22.8.2;8.2 Regularisation Parameters;602
1.22.8.3;8.3 Effect of Radiation Reaction on the Waveforms During Plunge;602
1.22.9;9 Beyond the State of the Art: the Self-Consistent Prescription;603
1.22.10;10 Conclusions;605
1.22.11;References;607
1.23;Index;614