Essays in General Relativity - 1st Edition - ISBN: 9780126913804, 9781483273624

Essays in General Relativity

1st Edition

A Festschrift for Abraham Taub

Editors: Frank J. Tipler
eBook ISBN: 9781483273624
Imprint: Academic Press
Published Date: 1st January 1980
Page Count: 244
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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


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


2 Comments on the Topology of Nonsingular Stellar Models

I. Introduction

II. The Topology of Initially Newtonian Stars

III. The Topology of Primordial Stars


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


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


5 The Beam and Stay of the Taub Universe

Addendum on Lethal Radiation



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


7 Symmetry Breaking in General Relativity


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


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


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


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


12 Lagrangian Relativistic Hydrodynamics with Eulerian Coordinates

I. Introduction

II. General Formalism

III. Numerical Scheme


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


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


15 A Remark on Time-Independent Axisymmetric Fields


16 Values and Arguments in Homogeneous Spaces

I. Introduction

II. Homogeneous Cosmologies

III. Harmonic Maps


Curriculum Vitae of Abraham Haskel Taub

List of Publications


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© Academic Press 1980
Academic Press
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About the Editor

Frank J. Tipler

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