Essays in General Relativity

To Abe Taub, the Universe Man PoemThe Taub UniverseList of ContributorsPreface1 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 References2 Comments on the Topology of Nonsingular Stellar Models I. Introduction II. The Topology of Initially Newtonian Stars III. The Topology of Primordial Stars References3 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 References4 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 References5 The Beam and Stay of the Taub Universe Addendum on Lethal Radiation Appendix References6 Tidal Forces in a Highly Asymmetric Taub Universe I. Introduction II. The Beam and Stay of the Taub Metric III. Cosmic Tides IV. Conclusion References7 Symmetry Breaking in General Relativity References8 Gauge Invariant Perturbation Theory in Spatially Homogeneous Cosmology I. Introduction II. Spatially Homogeneous Spacetimes III. ¿-Spin and Spherical Bases IV. Linearized Hamiltonian for Vacuum LRS Spatially Homogeneous Spacetimes V. Harmonic Analysis VI. The Moncrief Decomposition References9 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 References10 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 References11 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 References12 Lagrangian Relativistic Hydrodynamics with Eulerian Coordinates I. Introduction II. General Formalism III. Numerical Scheme References13 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 References14 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 References15 A Remark on Time-Independent Axisymmetric Fields References16 Values and Arguments in Homogeneous Spaces I. Introduction II. Homogeneous Cosmologies III. Harmonic Maps ReferencesCurriculum Vitae of Abraham Haskel TaubList of Publications