Essays in General Relativity
A Festschrift for Abraham Taub
- 1st Edition - January 1, 1980
- Editor: Frank J. Tipler
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 6 9 1 3 8 0 - 4
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 7 5 3 - 3
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 3 6 2 - 4
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… Read more
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Request a sales quoteEssays 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.
To Abe Taub, the Universe Man Poem
The Taub Universe
List of Contributors
Preface
1 On Schwarzschild Causality—A Problem for Lorentz Covariante General Relativity
I. Introduction
II. Lorentz Covariance and Causality
III. Schwarzschild Geometry
IV. The Theorem
V. Concluding Remarks
References
2 Comments on the Topology of Nonsingular Stellar Models
I. Introduction
II. The Topology of Initially Newtonian Stars
III. The Topology of Primordial Stars
References
3 General Relativity and the Eternal Return
I. Introduction
II. Brief History of the Eternal Return Idea
III. The No-Return Theorem
IV. Proof of the No-Return Theorem
V. Significance of the No-Return Theorem
References
4 Energy and Momentum of the Gravitational Field
I. Introduction
II. Asymptotically Flat Initial Data
III. Energy and Linear Momentum
IV. Boosted Schwarzchild Initial Data
V. The Positive Energy Conjecture
VI. Conditions on the Stress-Energy Tensor
V. Angular Momentum
References
5 The Beam and Stay of the Taub Universe
Addendum on Lethal Radiation
Appendix
References
6 Tidal Forces in a Highly Asymmetric Taub Universe
I. Introduction
II. The Beam and Stay of the Taub Metric
III. Cosmic Tides
IV. Conclusion
References
7 Symmetry Breaking in General Relativity
References
8 Gauge Invariant Perturbation Theory in Spatially Homogeneous Cosmology
I. Introduction
II. Spatially Homogeneous Spacetimes
III. ξ-Spin and Spherical Bases
IV. Linearized Hamiltonian for Vacuum LRS Spatially Homogeneous Spacetimes
V. Harmonic Analysis
VI. The Moncrief Decomposition
References
9 Locally Isotrophic Space-Time Nonnull Homogeneous Hypersurfaces
I. Introduction
II. Description of the Calculation Technique
III. Locally Rotationally Symmetric Space-Times
IV. Locally Boost Symmetric Spaces
V. Locally Null-Rotation-Symmetric Spaces
VI. The Ricci and Weyl Tensors
References
10 The Gravitational Waves That Bathe the Earth: Upper Limits Based on Theorists' Cherished Beliefs
I. Introduction
II. Cherished Beliefs
III. Upper Limits on Stochastic Background
IV. Upper Limits on Waves from Discrete Sources
V. Discussion
Appendix: Notation
References
11 General Relativistic Hydrodynamics: The Comoving, Eulerian, and Velocity Potential Formalisms
I. Introduction
II. Kinematics of Flows on Spacetime
III. Hydrodynamics and Thermodynamics
IV. Lagrangian or Comoving Coordinates
V. Eulerian or Noncomoving Coordinates
VI. The Velocity Potential Formalism
VII. Conclusions
References
12 Lagrangian Relativistic Hydrodynamics with Eulerian Coordinates
I. Introduction
II. General Formalism
III. Numerical Scheme
References
13 Some Thoughts on the Origin of Cosmic Inhomogeneities
I. Introduction
II. Current Observational Results
III. Linear Perturbations of Uniform Models
IV. Nonlinear Inhomogeneities in Fireball Phase
V. Hints of a Gravithermal Origin
VI. Summary
References
14 Automorphisms of Formal Algebras Associated by Deformation with a Symplectic Manifold
I. Classical Dynamics and Symplectic Manifolds
II. The Formal Algebras
III. Deformations and Cohomology
IV. Vey Algebras
V. Derivations and Class of Automorphisms for a Formal Lie Algebra
VI. Derivations of a Formal Associative Algebra
VII. Automorphisms of the Associative Algebra and of the Corresponding Lie Algebra
VIII. Automorphisms of an Associative Algebra which are Trivial Main Parts
IX. The Main Theorem
References
15 A Remark on Time-Independent Axisymmetric Fields
References
16 Values and Arguments in Homogeneous Spaces
I. Introduction
II. Homogeneous Cosmologies
III. Harmonic Maps
References
Curriculum Vitae of Abraham Haskel Taub
List of Publications
- No. of pages: 244
- Language: English
- Edition: 1
- Published: January 1, 1980
- Imprint: Academic Press
- Hardback ISBN: 9780126913804
- Paperback ISBN: 9781483247533
- eBook ISBN: 9781483273624
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