Tipler Essays in General Relativity

A Festschrift for Abraham Taub
1. Auflage 2013
ISBN: 978-1-4832-7362-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 244 Seiten, Web PDF

Essays in General Relativity: A Festschrift for Abraham Taub is collection of essays to honor Professor Abraham H. Taub on the occasion of his retirement from the mathematics faculty of the University of California at Berkeley. Relativistic hydrodynamics has always been a subject dear to Taub's heart. In fact, many basic results on special relativistic fluid flows are due to him, and he has been a major contributor to the study of fluid flows near shocks. The book contains 16 chapters and begins with a discussion of a geometrical approach to general relativity. This is followed by separate chapters that examine the topology of the space-time manifold representing a stellar model; the notion of an ''external return'' in the context of general relativity; and the standard two-surface integral formulation of gravitational energy and momentum. Subsequent chapters deal with tidal forces in a highly asymmetric Taub universe; derivation of theoretical upper limits on the strengths of the gravitational waves that bathe the Earth; and a new formulation of Lagrangian general relativistic hydrodynamics.

Autoren/Hrsg.

Tipler, Frank J.

Inhaltsverzeichnis

1;Front Cover;1
2;Essays in General Relativity: A Festschrift for Abraham Taub;4
3;Copyright Page;5
4;Table of Contents;10
5;Dedication;7
6;List of Contributors;16
7;Preface;18
8;Chapter 1. On Schwarzschild Causality—A Problem for "Lorentz Covariante" General Relativity;20
8.1;I. Introduction;20
8.2;II. Lorentz Covariance and Causality;21
8.3;III. Schwarzschild Geometry;23
8.4;IV. The Theorem;25
8.5;V. Concluding Remarks;30
8.6;Acknowledgment;30
8.7;References;30
9;Chapter 2. Comments on the Topology of Nonsingular Stellar Models;32
9.1;I. Introduction;32
9.2;II. The Topology of Initially Newtonian Stars;34
9.3;III. The Topology of Primordial Stars;36
9.4;Acknowledgment;38
9.5;References;38
10;Chapter 3. General Relativity and the Eternal Return;40
10.1;I. Introduction;40
10.2;II. Brief History of the Eternal Return Idea;42
10.3;III. The No-Return Theorem;47
10.4;IV. Proof of the No-Return Theorem;49
10.5;V. Significance of the No-Return Theorem;51
10.6;Acknowledgments;54
10.7;References;54
11;Chapter 4. Energy and Momentum of the Gravitational Field;58
11.1;I. Introduction;58
11.2;II. Asymptotically Flat Initial Data;59
11.3;III. Energy and Linear Momentum;62
11.4;IV. Boosted Schwarzschild Initial Data;64
11.5;V. The Positive Energy Conjecture;67
11.6;VI. Conditions on the Stress-Energy Tensor;71
11.7;VII. Angular Momentum;74
11.8;Acknowledgments;75
11.9;References;76
12;Chapter 5. The Beam and Stay of the Taub Universe;78
12.1;Addendum on Lethal Radiation;88
12.2;Appendix;88
12.3;References;89
13;Chapter 6. Tidal Forces in a Highly Asymmetric Taub Univers;90
13.1;I. Introduction;90
13.2;II. The Beam and Stay of the Taub Metric;91
13.3;III. Cosmic Tides;93
13.4;IV. Conclusion;95
13.5;References;96
14;Chapter 7. Symmetry Breaking in General Relativity;98
14.1;References;115
15;Chapter 8. Gauge Invariant Perturbation Theory in Spatially Homogeneous Cosmology;116
15.1;I. Introduction;116
15.2;II. Spatially Homogeneous Spacetimes;118
15.3;III. .-spin and Spherical Bases;120
15.4;IV. Linearized Hamiltonian for Vacuum LRS Spatially Homogeneous Spacetimes;127
15.5;V. Harmonic Analysis;131
15.6;VI. The Moncrief Decomposition;135
15.7;References;138
16;Chapter 9. Locally Isotropie Space-Times with Nonnull Homogeneous Hypersurfaces;140
16.1;I. Introduction;140
16.2;II. Description of the Calculation Technique;142
16.3;III. Locally Rotationally Symmetric Space-Times;146
16.4;IV. Locally Boost Symmetric Spaces;148
16.5;V. Locally Null-Rotation-Symmetric Spaces;150
16.6;VI. The Ricci and Weyl Tensors;152
16.7;VII. Further Remarks;155
16.8;Acknowledgments;156
16.9;References;156
17;Chapter 10. The Gravitational Waves That Bathe the Earth : Upper Limits Based on Theorists' Cherished Beliefs;158
17.1;I. Introduction;158
17.2;II. Cherished Beliefs;160
17.3;III. Upper Limits on Stochastic Background;164
17.4;IV. Upper Limits on Waves from Discrete Sources;167
17.5;V. Discussion;171
17.6;Acknowledgment;173
17.7;References;173
18;Chapter 11. General Relativistic Hydrodynamics: The Comoving, Eulerian, and Velocity Potential Formalisms;176
18.1;I. Introduction;177
18.2;II. Kinematics of Flows on Spacetime;177
18.3;III. Hydrodynamics and Thermodynamics;180
18.4;IV. Lagrangian or Comoving Coordinates;183
18.5;V. Eulerian or Noncomoving Coordinates;189
18.6;VI. The Velocity Potential Formalism;198
18.7;VII. Conclusions;200
18.8;Acknowledgments;200
18.9;References;201
19;Chapter 12. Lagrangian Relativistic Hydrodynamics with Eulerian Coordinates;204
19.1;I. Introduction;204
19.2;II. General Formalism;205
19.3;III. Numerical Scheme;207
19.4;Acknowledgments;208
19.5;References;208
20;Chapter 13. Some Thoughts on the Origin of Cosmic Inhomogeneities;210
20.1;I. Introduction;210
20.2;II. Current Observational Results;211
20.3;III. Linear Perturbations of Uniform Models;213
20.4;IV. Nonlinear Inhomogeneities in Fireball Phase;215
20.5;V. Hints of a Gravithermal Origin;218
20.6;VI. Summary;220
20.7;References;220
21;Chapter 14. Automorphisms of Formal Algebras Associated by Deformation with a Symplectic Manifold;222
21.1;I. Classical Dynamics and Symplectic Manifolds;222
21.2;II. The Formal Algebras;224
21.3;III. Deformations and Cohomology;225
21.4;IV. Vey Algebras;228
21.5;V. Derivations and Class of Automorphisms for a Formal Lie Algebra;229
21.6;VI. Derivations of a Formal Associative Algebra;231
21.7;VII. Automorphisms of the Associative Algebra and of the Corresponding Lie Algebra;232
21.8;VIII. Automorphisms of an Associative Algebra which Are Trivial Main Parts;233
21.9;IX. The Main Theorem;234
21.10;References;235
22;Chapter 15. A Remark on Time-Independent Axisymmetric Fields;236
22.1;References;239
23;Chapter 16. Values and Arguments in Homogeneous Spaces;240
23.1;I. Introduction;241
23.2;II. Homogeneous Cosmologies;242
23.3;III. Harmonic Maps;244
23.4;References;249
24;Curriculum Vitae of Abraham Haskel Taub;251
25;List of Publications by A. H. Taub;252
26;Books Edited by A. H. Taub;255