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Einstein's Field Equations and Their Physical Implications : Selected Essays in Honour of Ja1/4rgen Ehlers :  Selected Essays in Honour of Ja1/4rgen Ehlers - Bernd G. Schmidt

Einstein's Field Equations and Their Physical Implications : Selected Essays in Honour of Ja1/4rgen Ehlers

Selected Essays in Honour of Ja1/4rgen Ehlers

By: Bernd G. Schmidt (Editor)

Hardcover Published: September 2007
ISBN: 9783540670735
Number Of Pages: 433

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This book serves two purposes. The authors present important aspects of modern research on the mathematical structure of Einstein's field equations & they show how to extract their physical content from them by mathematically exact methods. The essays are devoted to exact solutions & to the Cauchy problem of the field equations as well as to post-Newtonian approximations that have direct physical implications. Further topics concern quantum gravity & optics in gravitational fields. The book addresses researchers in relativity & differential geometry but can also be used as additional reading material for graduate students.

Selected Solutions of Einstein's Field Equations: Their Role in General Relativity and Astrophysicsp. 1
Introduction and a Few Excursionsp. 1
A Word on the Role of Explicit Solutions in Other Parts of Physics and Astrophysicsp. 3
Einstein's Field Equationsp. 5
"Just So" Notes on the Simplest Solutions: The Minkowski, de Sitter, and Anti-de Sitter Spacetimesp. 8
On the Interpretation and Characterization of Metricsp. 11
The Choice of Solutionsp. 15
The Outlinep. 17
The Schwarzschild Solutionp. 19
Spherically Symmetric Spacetimesp. 19
The Schwarzschild Metric and Its Role in the Solar Systemp. 20
Schwarzschild Metric Outside a Collapsing Starp. 21
The Schwarzschild-Kruskal Spacetimep. 25
The Schwarzschild Metric as a Case Against Lorentz-Covariant Approachesp. 28
The Schwarzschild Metric and Astrophysicsp. 29
The Reissner-Nordström Solutionp. 31
Reissner-Nordström Black Holes and the Question of Cosmic Censorshipp. 32
On Extreme Black Holes, d-Dimensional Black Holes, String Theory and "All That"p. 39
The Kerr Metricp. 42
Basic Featuresp. 42
The Physics and Astrophysics Around Rotating Black Holesp. 47
Astrophysical Evidence for a Kerr Metricp. 50
Black Hole Uniqueness and Multi-black Hole Solutionsp. 52
On Stationary Axisymmetric Fields and Relativistic Disksp. 55
Static Weyl Metricsp. 55
Relativistic Disks as Sources of the Kerr Metric and Other Stationary Spacetimesp. 57
Uniformly Rotating Disksp. 59
Taub-NUT Spacep. 62
A New Way to the NUT Metricp. 62
Taub-NUT Pathologies and Applicationsp. 64
Plane Waves and Their Collisionsp. 66
Plane-Fronted Wavesp. 66
Plane-Fronted Waves: New Developments and Applicationsp. 71
Colliding Plane Wavesp. 72
Cylindrical Wavesp. 77
Cylindrical Waves and the Asymptotic Structure of 3-Dimensional General Relativityp. 78
Cylindrical Waves and Quantum Gravityp. 82
Cylindrical Waves: a Miscellanyp. 85
On the Robinson-Trautman Solutionsp. 86
The Boost-Rotation Symmetric Radiative Spacetimesp. 88
The Cosmological Modelsp. 93
Spatially Homogeneous Cosmologiesp. 95
Inhomogeneous Cosmologiesp. 102
Concluding Remarksp. 105
Referencesp. 108
The Cauchy Problem for the Einstein Equationsp. 127
Introductionp. 127
Basic Observations and Conceptsp. 131
The Principal Symbolp. 132
The Constraintsp. 135
The Bianchi Identitiesp. 137
The Evolution Equationsp. 137
Assumptions and Consequencesp. 146
PDE Techniquesp. 147
Symmetric Hyperbolic Systemsp. 147
Symmetric Hyperbolic Systems on Manifoldsp. 157
Other Notions of Hyperbolicityp. 159
Reductionsp. 164
Hyperbolic Systems from the ADM Equationsp. 167
The Einstein-Euler Systemp. 173
The Initial Boundary Value Problemp. 185
The Einstein-Dirac Systemp. 193
Remarks on the Structure of the Characteristic Setp. 200
Local Evolutionp. 201
Local Existence Theorems for the Einstein Equationsp. 201
Uniquenessp. 204
Cauchy Stabilityp. 206
Matter Modelsp. 207
An Example of an Ill-Posed Initial Value Problemp. 214
Symmetriesp. 216
Outlookp. 217
Referencesp. 219
Post-Newtonian Gravitational Radiationp. 225
Introductionp. 225
On Approximation Methods in General Relativityp. 225
Field Equations and the No-Incoming-Radiation Conditionp. 228
Method and General Physical Picturep. 231
Multipole Decompositionp. 233
The Matching Equationp. 233
The Field in Terms of Multipole Momentsp. 236
Equivalence with the Will-Wiseman Multipole Expansionp. 238
Source Multipole Momentsp. 240
Multipole Expansion in Symmetric Trace-Free Formp. 240
Linearized Approximation to the Exterior Fieldp. 241
Derivation of the Source Multipole Momentsp. 242
Post-Minkowskian Approximationp. 244
Multipolar Post-Minkowskian Iteration of the Exterior Fieldp. 244
The "Canonical" Multipole Momentsp. 246
Retarded Integral of a Multipolar Extended Sourcep. 247
Radiative Multipole Momentsp. 248
Definition and General Structurep. 249
The Radiative Quadrupole Moment to 3PN Orderp. 250
Tail Contributions in the Total Energy Fluxp. 251
Post-Newtonian Approximationp. 253
The Inner Metric to 2.5PN Orderp. 254
The Mass-Type Source Moment to 2.5PN Orderp. 256
Point-Particlesp. 258
Hadamard Partie Finie Regularizationp. 259
Multipole Moments of Point-Mass Binariesp. 261
Equations of Motion of Compact Binariesp. 263
Gravitational Waveforms of Inspiralling Compact Binariesp. 265
Conclusionp. 267
Duality and Hidden Symmetries in Gravitational Theoriesp. 273
Introductionp. 273
Electromagnetic Dualityp. 277
Duality in Kaluza-Klein Theoriesp. 279
Dimensional Reduction from D to d Dimensionsp. 280
Reduction to d = 4 Dimensionsp. 282
Reduction to d =3 Dimensionsp. 285
Reduction to d = 2 Dimensionsp. 290
Geroch Groupp. 292
Stationary Black Holesp. 302
Spherically Symmetric Solutionsp. 306
Uniqueness Theorems for Static Black Holesp. 312
Stationary, Axially Symmetric Black Holesp. 314
Acknowledgmentsp. 316
Non-linear ¿-Models and Symmetric Spacesp. 316
Non-compact Riemannian Symmetric Spacesp. 316
Pseudo-Riemannian Symmetric Spacesp. 319
Consistent Truncationsp. 319
Structure of the Lie Algebrap. 319
Time-Independent Gravitational Fieldsp. 325
Introductionp. 325
Field Equationsp. 327
Generalitiesp. 327
Axial Symmetryp. 333
Asymptotic Flatness: Lichnerowicz Theoremsp. 334
Newtonian Limitp. 339
Existence Issues and the Newtonian Limitp. 340
Far Fieldsp. 341
Far-Field Expansionsp. 341
Conformal Treatment of Infinity, Multipole Momentsp. 344
Global Rotating Solutionsp. 350
Lindblom's Theoremp. 350
Existence of Stationary Rotating Axi-symmetric Fluid Bodiesp. 353
The Neugebauer-Meinel Diskp. 357
Global Non-rotating Solutionsp. 360
Elastic Static Bodiesp. 360
Are Perfect Fluids O (3)-Symmetric?p. 362
Spherically Symmetric, Static Perfect Fluid Solutionsp. 365
Spherically Symmetric, Static Einstein-Vlasov Solutionsp. 370
Gravitational Lensing from a Geometric Viewpointp. 373
Introductionp. 373
Some Basic Notions of Spacetime Geometryp. 375
Gravitational Lensing in Arbitrary Spacetimesp. 378
Conjugate Points and Cut Pointsp. 381
The Geometry of Light Conesp. 385
Citeria for Multiple Imagingp. 391
Fermat's Principlep. 396
Morse Index Theory for Fermat's Principlep. 399
Gravitational Lensing in Globally Hyperbolic Spacetimesp. 403
Criteria for Multiple Imaging in Globally Hyperbolic Spacetimesp. 405
Morse Theory in Globally Hyperbolic Spacetimesp. 408
Gravitational Lensing in Asymptotically Simple and Empty Spacetimesp. 414
Referencesp. 422
Jürgen Ehlers - Bibliographyp. 427
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540670735
ISBN-10: 3540670734
Series: Lecture Notes in Physics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 433
Published: September 2007
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 2.54
Weight (kg): 0.81

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