Essays in General Relativity (eBook)

Front Cover 1
Essays in General Relativity: A Festschrift for Abraham Taub 4
Copyright Page 5
Table of Contents 10
Dedication 7
List of Contributors 16
Preface 18
Chapter 1. On Schwarzschild Causality—A Problem for "Lorentz Covariante" General Relativity 20
I. Introduction 20
II. Lorentz Covariance and Causality 21
III. Schwarzschild Geometry 23
IV. The Theorem 25
V. Concluding Remarks 30
Acknowledgment 30
References 30
Chapter 2. Comments on the Topology of Nonsingular Stellar Models 32
I. Introduction 32
II. The Topology of Initially Newtonian Stars 34
III. The Topology of Primordial Stars 36
Acknowledgment 38
References 38
Chapter 3. General Relativity and the Eternal Return 40
I. Introduction 40
II. Brief History of the Eternal Return Idea 42
III. The No-Return Theorem 47
IV. Proof of the No-Return Theorem 49
V. Significance of the No-Return Theorem 51
Acknowledgments 54
References 54
Chapter 4. Energy and Momentum of the Gravitational Field 58
I. Introduction 58
II. Asymptotically Flat Initial Data 59
III. Energy and Linear Momentum 62
IV. Boosted Schwarzschild Initial Data 64
V. The Positive Energy Conjecture 67
VI. Conditions on the Stress-Energy Tensor 71
VII. Angular Momentum 74
Acknowledgments 75
References 76
Chapter 5. The Beam and Stay of the Taub Universe 78
Addendum on Lethal Radiation 88
Appendix 88
References 89
Chapter 6. Tidal Forces in a Highly Asymmetric Taub Univers 90
I. Introduction 90
II. The Beam and Stay of the Taub Metric 91
III. Cosmic Tides 93
IV. Conclusion 95
References 96
Chapter 7. Symmetry Breaking in General Relativity 98
References 115
Chapter 8. Gauge Invariant Perturbation Theory in Spatially Homogeneous Cosmology 116
I. Introduction 116
II. Spatially Homogeneous Spacetimes 118
III. .-spin and Spherical Bases 120
IV. Linearized Hamiltonian for Vacuum LRS Spatially Homogeneous Spacetimes 127
V. Harmonic Analysis 131
VI. The Moncrief Decomposition 135
References 138
Chapter 9. Locally Isotropie Space-Times with Nonnull Homogeneous Hypersurfaces 140
I. Introduction 140
II. Description of the Calculation Technique 142
III. Locally Rotationally Symmetric Space-Times 146
IV. Locally Boost Symmetric Spaces 148
V. Locally Null-Rotation-Symmetric Spaces 150
VI. The Ricci and Weyl Tensors 152
VII. Further Remarks 155
Acknowledgments 156
References 156
Chapter 10. The Gravitational Waves That Bathe the Earth : Upper Limits Based on Theorists' Cherished Beliefs 158
I. Introduction 158
II. Cherished Beliefs 160
III. Upper Limits on Stochastic Background 164
IV. Upper Limits on Waves from Discrete Sources 167
V. Discussion 171
Acknowledgment 173
References 173
Chapter 11. General Relativistic Hydrodynamics: The Comoving, Eulerian, and Velocity Potential Formalisms 176
I. Introduction 177
II. Kinematics of Flows on Spacetime 177
III. Hydrodynamics and Thermodynamics 180
IV. Lagrangian or Comoving Coordinates 183
V. Eulerian or Noncomoving Coordinates 189
VI. The Velocity Potential Formalism 198
VII. Conclusions 200
Acknowledgments 200
References 201
Chapter 12. Lagrangian Relativistic Hydrodynamics with Eulerian Coordinates 204
I. Introduction 204
II. General Formalism 205
III. Numerical Scheme 207
Acknowledgments 208
References 208
Chapter 13. Some Thoughts on the Origin of Cosmic Inhomogeneities 210
I. Introduction 210
II. Current Observational Results 211
III. Linear Perturbations of Uniform Models 213
IV. Nonlinear Inhomogeneities in Fireball Phase 215
V. Hints of a Gravithermal Origin 218
VI. Summary 220
References 220
Chapter 14. Automorphisms of Formal Algebras Associated by Deformation with a Symplectic Manifold 222
I. Classical Dynamics and Symplectic Manifolds 222
II. The Formal Algebras 224
III. Deformations and Cohomology 225
IV. Vey Algebras 228
V. Derivations and Class of Automorphisms for a Formal Lie Algebra 229
VI. Derivations of a Formal Associative Algebra 231
VII. Automorphisms of the Associative Algebra and of the Corresponding Lie Algebra 232
VIII. Automorphisms of an Associative Algebra which Are Trivial Main Parts 233
IX. The Main Theorem 234
References 235
Chapter 15. A Remark on Time-Independent Axisymmetric Fields 236
References 239
Chapter 16. Values and Arguments in Homogeneous Spaces 240
I. Introduction 241
II. Homogeneous Cosmologies 242
III. Harmonic Maps 244
References 249
Curriculum Vitae of Abraham Haskel Taub 251
List of Publications by A. H. Taub 252
Books Edited by A. H. Taub 255