General Relativity and John Archibald Wheeler (eBook)

Ignazio Ciufolini, Richard A. Matzner (Herausgeber)

eBook Download: PDF

2010 | 2010
XIV, 548 Seiten
Springer Netherland (Verlag)
978-90-481-3735-0 (ISBN)

Infos

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.

Richard Matzner earned his Ph.D. in 1967 from The University of Maryland. He has been involved since then in questions of cosmology, of gravitational radiation, and of black hole physics. He has been Director of The Center for Relativity at The University of Texas at Austin since 1987. In 1993 he organized and became the Lead Principal Investigator of a NSF/ARPA funded eight-university Computational Grand Challenge program describing the interaction of black holes, which are potential sources for observable gravitational radiation. Matzner has served on a number of advisory committees to the Air Force, the National Science Foundation, the European Space Agency, and The Department of Energy. He is currently a member of High Performance Computing advisory and allocation committees, on campus, and nationally. In 1996-97 he was on research assignment at Los Alamos National Laboratory, in the Institute for Geophysics and Planetary Physics, where he began work on the Dictionary of Geophysics, Astrophysics, and Astronomy, to be published by CRC Press.

Ignazio Ciufolini worked with John Archibald Wheeler on the book 'Gravitation and Inertia' recipient of the US 'American Association of Publishers' Award for the best 1995 professional and scholar book in physics and astronomy. In 2001, he was awarded the International Tomassoni-Chisesi prize for physics by Sapienza University. Ciufolini, from the University of Salento, and Erricos Pavlis from the University of Maryland BC, analysed the orbits of the satellites LAGEOS and LAGEOS 2 and, in 2004, published in Nature the measurement, with an uncertainty of about 10 %, of the frame-dragging effect, predicted by Einstein's General Relativity. Commenting on this 2004 research, Neil Ashby of the University of Colorado, said the result was 'the first reasonably accurate measurement of frame dragging.' The reaction to this latest measurement has been broadly positive and, on 6th September 2007, Nature dedicated its cover to Ciufolini's research. He is currently the Principal Investigator of the LARES satellite to be launched in 2011 to test Einstein's theory.

Inhalt

Introduction to General Relativity and John Archibald Wheeler 15
1 John Archibald Wheeler and General Relativity 16
2 General Relativity and Its Tests 16
3 Gravitational Waves 17
4 Frame-Dragging and Gravitomagnetism 18
References 19
Part I John Archibald Wheeler and General Relativity 21
John Wheeler and the Recertification of General Relativity as True Physics 22
1 Introduction 22
2 John Archibald Wheeler 23
3 John A. Wheeler and the Renaissance of General Relativity 36
References 39
John Archibald Wheeler: A Few Highlights of His Contributions to Physics 41
References 49
Wheeler Wormholes and the Modern Astrophysics 51
1 Introduction 51
2 Wormholes and Their Remnants in the Universe 53
3 Wormholes and the Multi-universe 58
4 Conclusion 59
5 Appendixes 60
5.1 Spherically Symmetrical Wormhole with Radial Magnetic Field 60
5.2 Dipolar Electric Field Induced in a WH 64
5.3 Observations of Body Oscillating Through a WH Throat 65
5.4 Circular Orbit Around a WH 67
References 67
Part II Foundations and Tests of General Relativity 69
Unified Form of the Initial Value Conditions 70
1 Some Geometry and Notation 70
2 Einstein's Equations 73
3 The 3+1-Form of Einstein's Equations 75
4 Conformal Transformations 77
5 An Elliptic System 79
References 83
The Confrontation Between General Relativity and Experiment 84
1 Introduction 84
2 The Einstein Equivalence Principle 86
2.1 Tests of the Weak Equivalence Principle 86
2.2 Tests of Local Lorentz Invariance 89
2.3 Tests of Local Position Invariance 91
3 Solar-System Tests 92
3.1 The Parametrized Post-Newtonian Framework 92
3.2 Bounds on the PPN Parameters 94
3.3 Gravity Probe B 96
4 The Binary Pulsar 96
5 Gravitational-Wave Tests of Gravitation Theory 98
5.1 Polarization of Gravitational Waves 98
5.2 Speed of Gravitational Waves 99
6 Tests of Gravity in the Strong-Field Regime 100
7 Conclusions 101
References 102
Measurements of Space Curvature by Solar Mass 105
1 Introduction 105
2 Bending Experiments 106
2.1 Measurements During Solar Eclipse 108
2.2 Bending Measurements at Radio Frequencies 109
2.3 VLBI Measurements at Radio Frequencies 110
3 Spacecraft Radio Tracking Experiments 111
3.1 The Cassini 2002 Solar Conjunction Experiment 113
3.2 Data Processing and Data Analysis for the 2002 Cassini Experiment 113
References 116
Modern Cosmology: Early and Late Universe 119
1 ``Go There, Don't Know Where. Bring Me That, Don't Know What" 119
2 Early Universe and Late Universe 121
3 In the Beginning Was Sound. And the Sound Was of the Big Bang 123
4 Dark Side of Matter 127
5 On the Verge of New Physics 129
References 129
Part III Gravitational Waves 130
Introduction to Gravitational Waves 131
1 Introduction 131
2 Details of Einstein Equations 132
3 Linearized Einstein Equations: Weak Fields – Far from the Source 133
4 Linear Theory Coordinate Transformations More General Than Lorentz Small Coordinate Transformations
5 Gauge Invariance of the Riemann Tensor 135
6 Linearized Gravity and the Wave Equation 136
7 Effects of Gravitational Radiation 138
7.1 Riemann Tensor Depends Only on Transverse Traceless Components 139
7.2 Do Gravitational Waves Carry Energy? 139
8 Detection of Gravitational Waves 140
9 Strength of Gravitational Waves 142
9.1 Estimate of Typical Gravitational Radiation 143
10 Computing Gravitational Wave Signals 146
11 Coordinates for Computational Relativity 148
12 Space+Time (3+1) Coordinates 149
12.1 Outer Boundary Conditions for Space+Time Computations 150
13 The Einstein Equations for Space+Time Formulations 150
14 Fun with Exact Solutions 151
14.1 Schwarzschild in Standard Coordinates 151
14.2 Schwarzschild in Kerr–Schild Coordinates 152
15 Creating Initial Data 152
16 Computational Evolution of Binary Black Hole Systems 153
17 Conclusion 157
References 157
Discovering Relic Gravitational Waves in Cosmic Microwave Background Radiation 159
1 Introduction 159
2 Cosmological Oscillators 164
3 Quantization of Gravitational Waves 167
4 Squeezing and Power Spectrum 172
5 Density Perturbations 177
6 Quantization of Density Perturbations 182
7 What Inflationary Theory Says About Density Perturbations, and What Should be said About Inflationary Theory 184
8 Why Relic Gravitational Waves should be Detectable 191
9 Intensity and Polarization of the CMB Radiation 193
10 Radiative Transfer in a Perturbed Universe 195
11 Statistics and Angular Correlation Functions 196
12 Temperature-Polarization Cross-Correlation Function 201
13 Prospects of the Current and Forthcoming Observations 205
References 206
Status of Gravitational Wave Detection 208
1 INFN – Pisa and European Gravitational Observatory 208
2 The Generation of Gravitational Waves 209
3 The v Reduction 210
4 The Detection of GW 212
5 Short Outline About GW Sources 213
6 Modern Bar Detectors: Cryogenic Bars 218
7 Spherical Detectors 223
8 Interferometric Detectors 226
9 Interferometer Noises 228
10 Modern Interferometers with QND Signal Readout 230
11 The Network of Interferometric GW Detectors 245
12 Brief Status of GW Detection 256
13 The Future 261
References 272
Search for Gravitational Waves with Resonant Detectors 275
1 Introduction 275
2 Beginning of the Experimental Activity 278
3 Interaction of GW with Free Masses 279
4 The Cross-Section for a Resonant Bar 280
5 Algorithms for the Search of Short Bursts 281
5.1 The ZOP Filter 281
5.2 The Wiener Filter 283
6 The Matched Filter 285
7 Sensitivity and Bandwidth 288
8 Initial Experiments and the IGEC Collaboration 291
9 The EXPLORER and NAUTILUS Experiment 291
9.1 Calibration of the Rome Detectors 291
9.2 Experimental Apparatus 293
9.3 The Coincidence Window 295
9.4 Experimental Results 296
10 Conclusion 298
References 299
Gravitational Fields with 2-Dimensional Killing Leaves and the Gravitational Interaction of Light 302
1 Introduction 302
2 Geometric Aspects 304
2.1 Einstein Metrics When g(Y,Y)0 305
2.1.1 Canonical Form of Metrics When g(Y,Y)0 305
2.1.2 Normal Form of Metrics When g(Y,Y)0 306
2.2 Einstein Metrics When g(Y,Y)=0 306
3 Global Solutions 307
3.1 zeta-Complex Structures 309
3.2 Global Properties of Solutions 311
4 Examples 312
4.1 Algebraic Solutions 312
4.2 Info-Holes 312
4.3 A Star ``Outside" the Universe 313
5 Physical Properties 313
5.1 Spin-1 Gravitational Waves 314
5.2 The Standard Linearized Theory 315
5.3 Asymptotic Flatness and Matter Sources 318
5.4 More on the Wave Character of the Field 319
6 Final Remarks 320
7 Appendix: The Petrov Classification 321
7.1 Newman–Penrose Formalism 322
7.2 The Petrov Classification and the Newman–Penrose Formalism 323
References 324
Part IV Frame Dragging and Gravitomagnetism 327
Rotation and Spin in Physics 328
1 Introduction 328
2 Newtonian Classical Physics 329
3 Special Relativity 331
4 Quantum Mechanics 332
5 Quantum Electrodynamics (QED) 333
6 General Relativity 334
7 Conclusions 337
References 338
The Gravitomagnetic Influence on Earth-Orbiting Spacecrafts and on the Lunar Orbit 340
References 345
Quasi-inertial Coordinates 347
1 Introduction 347
2 Fermi–Walker Transport of a Tetrad 349
3 Fixed and Orbiting Gyroscopes 352
4 Construction of Quasi-inertial Coordinates 354
4.1 The Basis Tetrad 356
4.2 Coordinate Transformations 357
4.3 Metric in the Quasi-inertial Frame 358
5 Spin Precession in the Quasi-inertial Frame 360
6 Aberration 362
7 Two Sources – Sun and Earth 364
8 Local Inertial Frame of Earth 366
9 Quasi-inertial Coordinates in the Gödel Universe 369
10 Summary 372
References 372
Gravitomagnetism and Its Measurement with Laser Ranging to the LAGEOS Satellites and GRACE Earth Gravity Models 373
1 Dragging of Inertial Frames and Gravitomagnetism 374
2 An Invariant Characterization of Gravitomagnetism 377
3 Measurement of Gravitomagnetism with the LAGEOS Satellites and the GRACE Earth Gravity Models 382
3.1 Method of the 2004 Analysis with LAGEOS, LAGEOS 2 and the GRACE Models 383
4 GRACE and Its Gravity Field Models 387
5 Results: Measurement of the Lense–Thirring Effect and Its Uncertainty 389
5.1 Error Budget 389
5.2 Results of the Measurement of the Lense–Thirring Effect 392
6 The Error due to Earth's Gravity Field Uncertainties and a Realistic Assessment of the Accuracy of the GRACE Earth Gravity Models 397
6.1 On the Accuracy of GRACE-Based Models 397
6.2 The EIGEN-GRACE Series of Models from GFZ 400
6.3 The Independence of Errors and the Quality of Secular Zonal Rates 400
7 Conclusions 402
8 Appendix 1: Error Analysis 403
8.1 Gravitational Perturbations 404
8.1.1 Static Gravitational Field – Even Zonals 404
8.1.2 Odd Zonal Harmonics 406
8.1.3 Tides and Other Variations in the Gravity Field 406
8.2 Non-Gravitational Forces 413
8.2.1 Drag-Like Forces 413
8.2.2 Radiation Pressure 413
8.2.3 Albedo 414
8.2.4 Satellite Eclipses 415
8.2.5 Yarkovsky–Schach and Yarkovsky–Rubincam Effects 416
8.3 Other Error Sources 418
8.4 Summary of Error Budget 420
9 Appendix 2: Some Comments on the Error Analysis and Error Budget of the Gravitomagnetism Measurements with LAGEOS and LAGEOS 2 420
10 Appendix 3. Inclination Errors and Atmospheric Delay Modeling Uncertainties in SLR 426
References 430
The Relativity Mission Gravity Probe B, Testing Einstein's Universe 437
1 Introduction 437
2 The GP-B Experiment 439
3 GP-B Performance 442
4 GP-B, LISA, STEP 459
5 Lessons Learned 460
6 Improving Drag-Free: The Modular Gravitational Reference Sensor 463
7 Conclusions 466
References 467
The LARES Space Experiment: LARES Orbit, Error Analysis and Satellite Structure 469
1 Introduction 470
2 A New Laser-Ranged Satellite at a Lower Altitude Than LAGEOS and LAGEOS 2 472
3 Gravitational Uncertainties and Even Zonal Harmonics 477
4 Technical and Engineering Aspects of LARES Mission 480
4.1 Laser Ranging 480
4.2 Cube Corner Reflectors 480
4.3 LARES Satellite 484
4.4 Separation System 487
4.5 Launch Vehicle 489
5 Conclusions 490
References 491
The History of the So-Called Lense–Thirring Effect,and of Related Effects 495
1 The History of the So-Called Lense–Thirring Effect 495
2 Thirring's Work on the Rotating Mass Shell, and the Problem of a Correct Centrifugal Acceleration 500
3 Generalizations to Cosmological Models, and to Linearly Accelerated Mass Shells 503
References 504
Part V Miscellaneous 506
Atom Interferometers and Optical Clocks: New Quantum Sensors Based on Ultracold Atoms for Gravitational Tests in Earth Laboratories and in Space 507
1 Introduction 507
2 Precision Gravity Measurements by Atom Interferometry: Measurement of G and Test of Newtonian Law at Micrometric Distances 508
2.1 Measurement of G 508
2.2 Testing the Newtonian Gravity Law 511
3 Optical Atomic Clocks 514
References 515
The York Map and the Role of Non-inertial Frames in the Geometrical View of the Gravitational Field 517
References 528
Erratum 532
Index 533

Produkt-Details

• Erscheint lt. Verlag: 22.6.2010
• Reihe/Serie: Astrophysics and Space Science Library
• Reihe/Serie: Astrophysics and Space Science Library
• Zusatzinfo: XIV, 548 p. 22 illus. in color.
• Verlagsort: Dordrecht
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Relativitätstheorie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Themenwelt: Technik
• Schlagworte: astrophysics • Cosmology • Frame dragging • General relativity • Gravitation • gravitational waves • gravitomagnetism • Gravity • John Archibald Wheeler • Relativity • Universe
• ISBN-10: 90-481-3735-7 / 9048137357
• ISBN-13: 978-90-481-3735-0 / 9789048137350