Ciufolini General Relativity and John Archibald Wheeler

1. Auflage 2010
ISBN: 978-90-481-3735-0
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 548 Seiten

Observational and experimental data pertaining to gravity and cosmology are changing our view of the Universe. General relativity is a fundamental key for the understanding of these observations and its theory is undergoing a continuing enhancement of its intersection with observational and experimental data. These data include direct observations and experiments carried out in our solar system, among which there are direct gravitational wave astronomy, frame dragging and tests of gravitational theories from solar system and spacecraft observations.

This book explores John Archibald Wheeler's seminal and enduring contributions in relativistic astrophysics and includes: the General Theory of Relativity and Wheeler's influence; recent developments in the confrontation of relativity with experiments; the theory describing gravitational radiation, and its detection in Earth-based and space-based interferometer detectors as well as in Earth-based bar detectors; the mathematical description of the initial value problem in relativity and applications to modeling gravitational wave sources via computational relativity; the phenomenon of frame dragging and its measurement by satellite observations. All of these areas were of direct interest to Professor John A. Wheeler and were seminally influenced by his ideas.

Autoren/Hrsg.

Ciufolini, Ignazio

Inhaltsverzeichnis

1;Introduction to General Relativity and John Archibald Wheeler;15
1.1;1 John Archibald Wheeler and General Relativity;16
1.2;2 General Relativity and Its Tests;16
1.3;3 Gravitational Waves;17
1.4;4 Frame-Dragging and Gravitomagnetism;18
1.5;References;19
2;Part I John Archibald Wheeler and General Relativity;21
2.1;John Wheeler and the Recertification of General Relativity as True Physics;22
2.1.1;1 Introduction;22
2.1.2;2 John Archibald Wheeler;23
2.1.3;3 John A. Wheeler and the Renaissance of General Relativity;36
2.1.4;References;39
2.2;John Archibald Wheeler: A Few Highlights of His Contributions to Physics;41
2.2.1;References;49
2.3;Wheeler Wormholes and the Modern Astrophysics;51
2.3.1;1 Introduction;51
2.3.2;2 Wormholes and Their Remnants in the Universe;53
2.3.3;3 Wormholes and the Multi-universe;58
2.3.4;4 Conclusion;59
2.3.5;5 Appendixes;60
2.3.5.1;5.1 Spherically Symmetrical Wormhole with Radial Magnetic Field;60
2.3.5.2;5.2 Dipolar Electric Field Induced in a WH;64
2.3.5.3;5.3 Observations of Body Oscillating Through a WH Throat;65
2.3.5.4;5.4 Circular Orbit Around a WH;67
2.3.6;References;67
3;Part II Foundations and Tests of General Relativity;69
3.1;Unified Form of the Initial Value Conditions;70
3.1.1;1 Some Geometry and Notation;70
3.1.2;2 Einstein's Equations;73
3.1.3;3 The 3+1-Form of Einstein's Equations;75
3.1.4;4 Conformal Transformations;77
3.1.5;5 An Elliptic System;79
3.1.6;References;83
3.2;The Confrontation Between General Relativity and Experiment;84
3.2.1;1 Introduction;84
3.2.2;2 The Einstein Equivalence Principle;86
3.2.2.1;2.1 Tests of the Weak Equivalence Principle;86
3.2.2.2;2.2 Tests of Local Lorentz Invariance;89
3.2.2.3;2.3 Tests of Local Position Invariance;91
3.2.3;3 Solar-System Tests;92
3.2.3.1;3.1 The Parametrized Post-Newtonian Framework;92
3.2.3.2;3.2 Bounds on the PPN Parameters;94
3.2.3.3;3.3 Gravity Probe B;96
3.2.4;4 The Binary Pulsar;96
3.2.5;5 Gravitational-Wave Tests of Gravitation Theory;98
3.2.5.1;5.1 Polarization of Gravitational Waves;98
3.2.5.2;5.2 Speed of Gravitational Waves;99
3.2.6;6 Tests of Gravity in the Strong-Field Regime;100
3.2.7;7 Conclusions;101
3.2.8;References;102
3.3;Measurements of Space Curvature by Solar Mass;105
3.3.1;1 Introduction;105
3.3.2;2 Bending Experiments;106
3.3.2.1;2.1 Measurements During Solar Eclipse;108
3.3.2.2;2.2 Bending Measurements at Radio Frequencies;109
3.3.2.3;2.3 VLBI Measurements at Radio Frequencies;110
3.3.3;3 Spacecraft Radio Tracking Experiments;111
3.3.3.1;3.1 The Cassini 2002 Solar Conjunction Experiment;113
3.3.3.2;3.2 Data Processing and Data Analysis for the 2002 Cassini Experiment;113
3.3.4;References;116
3.4;Modern Cosmology: Early and Late Universe;119
3.4.1;1 ``Go There, Don't Know Where. Bring Me That, Don't Know What";119
3.4.2;2 Early Universe and Late Universe;121
3.4.3;3 In the Beginning Was Sound. And the Sound Was of the Big Bang;123
3.4.4;4 Dark Side of Matter;127
3.4.5;5 On the Verge of New Physics;129
3.4.6;References;129
4;Part III Gravitational Waves;130
4.1;Introduction to Gravitational Waves;131
4.1.1;1 Introduction;131
4.1.2;2 Details of Einstein Equations;132
4.1.3;3 Linearized Einstein Equations: Weak Fields – Far from the Source;133
4.1.4;4 Linear Theory Coordinate Transformations More General Than Lorentz; Small Coordinate Transformations;134
4.1.5;5 Gauge Invariance of the Riemann Tensor;135
4.1.6;6 Linearized Gravity and the Wave Equation;136
4.1.7;7 Effects of Gravitational Radiation;138
4.1.7.1;7.1 Riemann Tensor Depends Only on Transverse Traceless Components;139
4.1.7.2;7.2 Do Gravitational Waves Carry Energy?;139
4.1.8;8 Detection of Gravitational Waves;140
4.1.9;9 Strength of Gravitational Waves;142
4.1.9.1;9.1 Estimate of Typical Gravitational Radiation;143
4.1.10;10 Computing Gravitational Wave Signals;146
4.1.11;11 Coordinates for Computational Relativity;148
4.1.12;12 Space+Time (3+1) Coordinates;149
4.1.12.1;12.1 Outer Boundary Conditions for Space+Time Computations;150
4.1.13;13 The Einstein Equations for Space+Time Formulations;150
4.1.14;14 Fun with Exact Solutions;151
4.1.14.1;14.1 Schwarzschild in Standard Coordinates;151
4.1.14.2;14.2 Schwarzschild in Kerr–Schild Coordinates;152
4.1.15;15 Creating Initial Data;152
4.1.16;16 Computational Evolution of Binary Black Hole Systems;153
4.1.17;17 Conclusion;157
4.1.18;References;157
4.2;Discovering Relic Gravitational Waves in Cosmic Microwave Background Radiation;159
4.2.1;1 Introduction;159
4.2.2;2 Cosmological Oscillators;164
4.2.3;3 Quantization of Gravitational Waves;167
4.2.4;4 Squeezing and Power Spectrum;172
4.2.5;5 Density Perturbations;177
4.2.6;6 Quantization of Density Perturbations;182
4.2.7;7 What Inflationary Theory Says About Density Perturbations, and What Should be said About Inflationary Theory;184
4.2.8;8 Why Relic Gravitational Waves should be Detectable;191
4.2.9;9 Intensity and Polarization of the CMB Radiation;193
4.2.10;10 Radiative Transfer in a Perturbed Universe;195
4.2.11;11 Statistics and Angular Correlation Functions;196
4.2.12;12 Temperature-Polarization Cross-Correlation Function;201
4.2.13;13 Prospects of the Current and Forthcoming Observations;205
4.2.14;References;206
4.3;Status of Gravitational Wave Detection;208
4.3.1;1 INFN – Pisa and European Gravitational Observatory;208
4.3.2;2 The Generation of Gravitational Waves ;209
4.3.3;3 The v Reduction;210
4.3.4;4 The Detection of GW ;212
4.3.5;5 Short Outline About GW Sources;213
4.3.6;6 Modern Bar Detectors: Cryogenic Bars ;218
4.3.7;7 Spherical Detectors ;223
4.3.8;8 Interferometric Detectors ;226
4.3.9;9 Interferometer Noises;228
4.3.10;10 Modern Interferometers with QND Signal Readout ;230
4.3.11;11 The Network of Interferometric GW Detectors;245
4.3.12;12 Brief Status of GW Detection;256
4.3.13;13 The Future;261
4.3.14;References;272
4.4;Search for Gravitational Waves with Resonant Detectors;275
4.4.1;1 Introduction;275
4.4.2;2 Beginning of the Experimental Activity;278
4.4.3;3 Interaction of GW with Free Masses;279
4.4.4;4 The Cross-Section for a Resonant Bar;280
4.4.5;5 Algorithms for the Search of Short Bursts;281
4.4.5.1;5.1 The ZOP Filter;281
4.4.5.2;5.2 The Wiener Filter;283
4.4.6;6 The Matched Filter;285
4.4.7;7 Sensitivity and Bandwidth;288
4.4.8;8 Initial Experiments and the IGEC Collaboration;291
4.4.9;9 The EXPLORER and NAUTILUS Experiment;291
4.4.9.1;9.1 Calibration of the Rome Detectors;291
4.4.9.2;9.2 Experimental Apparatus;293
4.4.9.3;9.3 The Coincidence Window;295
4.4.9.4;9.4 Experimental Results;296
4.4.10;10 Conclusion;298
4.4.11;References;299
4.5;Gravitational Fields with 2-Dimensional Killing Leaves and the Gravitational Interaction of Light;302
4.5.1;1 Introduction;302
4.5.2;2 Geometric Aspects;304
4.5.2.1;2.1 Einstein Metrics When g(Y,Y)0;305
4.5.2.1.1;2.1.1 Canonical Form of Metrics When g(Y,Y)0;305
4.5.2.1.2;2.1.2 Normal Form of Metrics When g(Y,Y)0;306
4.5.2.2;2.2 Einstein Metrics When g(Y,Y)=0 ;306
4.5.3;3 Global Solutions;307
4.5.3.1;3.1 zeta-Complex Structures;309
4.5.3.2;3.2 Global Properties of Solutions;311
4.5.4;4 Examples;312
4.5.4.1;4.1 Algebraic Solutions;312
4.5.4.2;4.2 Info-Holes;312
4.5.4.3;4.3 A Star ``Outside" the Universe;313
4.5.5;5 Physical Properties;313
4.5.5.1;5.1 Spin-1 Gravitational Waves;314
4.5.5.2;5.2 The Standard Linearized Theory;315
4.5.5.3;5.3 Asymptotic Flatness and Matter Sources;318
4.5.5.4;5.4 More on the Wave Character of the Field;319
4.5.6;6 Final Remarks;320
4.5.7;7 Appendix: The Petrov Classification;321
4.5.7.1;7.1 Newman–Penrose Formalism;322
4.5.7.2;7.2 The Petrov Classification and the Newman–Penrose Formalism;323
4.5.8;References;324
5;Part IV Frame Dragging and Gravitomagnetism;327
5.1;Rotation and Spin in Physics;328
5.1.1;1 Introduction;328
5.1.2;2 Newtonian Classical Physics;329
5.1.3;3 Special Relativity;331
5.1.4;4 Quantum Mechanics;332
5.1.5;5 Quantum Electrodynamics (QED);333
5.1.6;6 General Relativity;334
5.1.7;7 Conclusions;337
5.1.8;References;338
5.2;The Gravitomagnetic Influence on Earth-Orbiting Spacecrafts and on the Lunar Orbit;340
5.2.1;References;345
5.3;Quasi-inertial Coordinates;347
5.3.1;1 Introduction;347
5.3.2;2 Fermi–Walker Transport of a Tetrad;349
5.3.3;3 Fixed and Orbiting Gyroscopes;352
5.3.4;4 Construction of Quasi-inertial Coordinates;354
5.3.4.1;4.1 The Basis Tetrad;356
5.3.4.2;4.2 Coordinate Transformations;357
5.3.4.3;4.3 Metric in the Quasi-inertial Frame;358
5.3.5;5 Spin Precession in the Quasi-inertial Frame;360
5.3.6;6 Aberration;362
5.3.7;7 Two Sources – Sun and Earth;364
5.3.8;8 Local Inertial Frame of Earth;366
5.3.9;9 Quasi-inertial Coordinates in the Gödel Universe;369
5.3.10;10 Summary;372
5.3.11;References;372
5.4;Gravitomagnetism and Its Measurement with Laser Ranging to the LAGEOS Satellites and GRACE Earth Gravity Models;373
5.4.1;1 Dragging of Inertial Frames and Gravitomagnetism;374
5.4.2;2 An Invariant Characterization of Gravitomagnetism;377
5.4.3;3 Measurement of Gravitomagnetism with the LAGEOS Satellites and the GRACE Earth Gravity Models;382
5.4.3.1;3.1 Method of the 2004 Analysis with LAGEOS, LAGEOS 2 and the GRACE Models;383
5.4.4;4 GRACE and Its Gravity Field Models;387
5.4.5;5 Results: Measurement of the Lense–Thirring Effect and Its Uncertainty;389
5.4.5.1;5.1 Error Budget;389
5.4.5.2;5.2 Results of the Measurement of the Lense–Thirring Effect;392
5.4.6;6 The Error due to Earth's Gravity Field Uncertainties and a Realistic Assessment of the Accuracy of the GRACE Earth Gravity Models;397
5.4.6.1;6.1 On the Accuracy of GRACE-Based Models;397
5.4.6.2;6.2 The EIGEN-GRACE Series of Models from GFZ;400
5.4.6.3;6.3 The Independence of Errors and the Quality of Secular Zonal Rates;400
5.4.7;7 Conclusions;402
5.4.8;8 Appendix 1: Error Analysis;403
5.4.8.1;8.1 Gravitational Perturbations;404
5.4.8.1.1;8.1.1 Static Gravitational Field – Even Zonals;404
5.4.8.1.2;8.1.2 Odd Zonal Harmonics;406
5.4.8.1.3;8.1.3 Tides and Other Variations in the Gravity Field;406
5.4.8.2;8.2 Non-Gravitational Forces;413
5.4.8.2.1;8.2.1 Drag-Like Forces;413
5.4.8.2.2;8.2.2 Radiation Pressure;413
5.4.8.2.3;8.2.3 Albedo;414
5.4.8.2.4;8.2.4 Satellite Eclipses;415
5.4.8.2.5;8.2.5 Yarkovsky–Schach and Yarkovsky–Rubincam Effects;416
5.4.8.3;8.3 Other Error Sources;418
5.4.8.4;8.4 Summary of Error Budget;420
5.4.9;9 Appendix 2: Some Comments on the Error Analysis and Error Budget of the Gravitomagnetism Measurements with LAGEOS and LAGEOS 2;420
5.4.10;10 Appendix 3. Inclination Errors and Atmospheric Delay Modeling Uncertainties in SLR;426
5.4.11;References;430
5.5;The Relativity Mission Gravity Probe B, Testing Einstein's Universe;437
5.5.1;1 Introduction;437
5.5.2;2 The GP-B Experiment;439
5.5.3;3 GP-B Performance;442
5.5.4;4 GP-B, LISA, STEP;459
5.5.5;5 Lessons Learned;460
5.5.6;6 Improving Drag-Free: The Modular Gravitational Reference Sensor;463
5.5.7;7 Conclusions;466
5.5.8;References;467
5.6;The LARES Space Experiment: LARES Orbit, Error Analysis and Satellite Structure;469
5.6.1;1 Introduction;470
5.6.2;2 A New Laser-Ranged Satellite at a Lower Altitude Than LAGEOS and LAGEOS 2;472
5.6.3;3 Gravitational Uncertainties and Even Zonal Harmonics;477
5.6.4;4 Technical and Engineering Aspects of LARES Mission;480
5.6.4.1;4.1 Laser Ranging;480
5.6.4.2;4.2 Cube Corner Reflectors ;480
5.6.4.3;4.3 LARES Satellite;484
5.6.4.4;4.4 Separation System ;487
5.6.4.5;4.5 Launch Vehicle;489
5.6.5;5 Conclusions;490
5.6.6;References;491
5.7;The History of the So-Called Lense–Thirring Effect,and of Related Effects;495
5.7.1;1 The History of the So-Called Lense–Thirring Effect;495
5.7.2;2 Thirring's Work on the Rotating Mass Shell, and the Problem of a Correct Centrifugal Acceleration;500
5.7.3;3 Generalizations to Cosmological Models, and to Linearly Accelerated Mass Shells;503
5.7.4;References;504
6;Part V Miscellaneous;506
6.1;Atom Interferometers and Optical Clocks: New Quantum Sensors Based on Ultracold Atoms for Gravitational Tests in Earth Laboratories and in Space;507
6.1.1;1 Introduction;507
6.1.2;2 Precision Gravity Measurements by Atom Interferometry: Measurement of G and Test of Newtonian Law at Micrometric Distances;508
6.1.2.1;2.1 Measurement of G;508
6.1.2.2;2.2 Testing the Newtonian Gravity Law;511
6.1.3;3 Optical Atomic Clocks;514
6.1.4;References;515
6.2;The York Map and the Role of Non-inertial Frames in the Geometrical View of the Gravitational Field;517
6.2.1;References;528
7;Erratum;532
8;Index;533