Relativity and the Question of Discretization in Astronomy

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Product Details

  • ISBN-13: 9783642880865
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 4/15/2012
  • Series: Springer Tracts in Natural Philosophy Series , #20
  • Edition description: Softcover reprint of the original 1st ed. 1970
  • Edition number: 1
  • Pages: 188
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.42 (d)

Table of Contents

Prologue.- One Theoretical Considerations.- I The Environment for Cosmic Structures.- A. The External or Cosmological Enveloping Environment.- 1. The Classical Models.- 2. Inhomogeneity as a Similarity Construct.- 3. The Momentum-Energy Tensor.- 4. The Governing Equations.- 5. The Dispersion Vector.- 6. Approximation: Prestructures.- 7. The Condition of Bounded Potential in the Classical Models.- 8. The Future State with Bounded Potential.- 9. Solution of the Prestructure Equation and the Resulting Inhomogeneities.- B. Internal Consistency Structure: The Locally Induced Environment.- 10. Observation Operators.- 11. From the Local to the Macroscopic.- 12. Implication and Inference.- II An Equilibrium Theory of Galactic Isopleths.- A. Geometric Equilibrium.- 13. Isopleths and Timelike Hypersurfaces.- 14. Geometric Equilibrium.- 15. Implications of Geometric Equilibrium.- B. Physical Isopleths and Jump Discontinuities.- 16. Surface Quantities and Continuity Assumptions.- 17. Jump Strengths and Existence Conditions.- 18. Differential Relations.- 19. The Continuation Problem.- 20. Solution of the Continuation Problem.- 21. Physical Identification of the Isopleths.- C. Physical Isopleths in Geometric Equilibrium.- 22. Determination of {S??}.- 23. More about {S??}.- 24. The Tsoplethic Condition and the Perfect Fluid Approximation.- 25. The Trace Condition and the Discretization Equation.- III Galactic Morphology and Scale.- A. The Underlying Geometry of S* and the Equations of the Isopleth.- 26. Interpretation of the— Function.- 27. The Subsidiary Space T.- 28. The Metric Tensor of T.- 29. The Embedding Problem.- 30. Spacelike Quadrics.- 31. Equations for the Isopleths.- B. The Discretization Equation.- 32. Normalization.- 33. Evaluation D.- 34. The Linearized Discretization Equation.- C. Equilibrium Morphology of E and SO Galaxies and the Scale Question.- 35. The Resulting Morphology of E and SO Galaxies.- 36. The Linear Scale.- 37. Galactic Scale Discretization.- Two Observational Considerations.- IV Observational Problems of Macroscale Discretization.- A. Epistemological Viewpoints.- 38. The Discrete and the Continuous.- 39. Paradigmatic Inference.- B. Design of Observational Tests.- 40. Tests for Discretization Hypotheses.- 41. Remarks on Statistical Tests.- V Observational Evidence for Discretization Phenomena.- A. Diameters of Galaxies.- 42. Measurement of Diameters.- 43. Discretization in Bright Galaxies.- 44. Discretization in Cluster Galaxies.- B. Redshift Discretizations.- 45. Prediction of Discretized Redshifts.- 46. Redshift Discretization of Clusters of Galaxies.- 47. Other Redshift Discretizations.- 48. Atomic-Cosmic Relations.- Appendix A. Curvature Conventions and Signs.- Appendix B. The Spherically Symmetric Case.- Appendix C. On Conformally Related Metric Spaces, One of which Admits an Irrotational Isometry.- 3. Lemma and Relations.- Appendix D. Analysis of the Complete Nonlinear Discretization Equation.- 1. Statement of the Problem.- 2. Conditions for Nontrivial Solutions.- 4. The First Approximation.- 5. The Second and Higher Order Approximations.- Author Index.

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