Essays in General Relativity

Essays in General Relativity

A Festschrift for Abraham Taub

1st Edition - January 1, 1980

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  • Editor: Frank J. Tipler
  • eBook ISBN: 9781483273624

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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

Product details

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

About the Editor

Frank J. Tipler

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