# Essays in General Relativity

### A Festschrift for Abraham Taub

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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.

## Table of Contents

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

## Product details

- No. of pages: 244
- Language: English
- Copyright: © Academic Press 1980
- Published: January 1, 1980
- Imprint: Academic Press
- eBook ISBN: 9781483273624