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Einstein, Hilbert, and the Theory of Gravitation


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Table of Contents

1. Introduction.- 2. Steps Towards a New Theory of Gravitation.- 2.1 The Principles of Equivalence and Relativity.- 2.2 Abraham’s Objections.- 2.3 Nordström’s Theory.- 2.4 Einstein and Grossmann: Search for the Mathematical Tools of General Relativity.- 2.5 The Foundation of General Relativity.- 3. Physics and Geometry.- 3.1 The Role of Axiomatization in Hilbert’s Work.- 3.2 Concepts of Space and Geometry.- 3.3 Space-Time and Invariants.- 3.4 Mie’s Field Theory of Matter.- 3.5 Hilbert’s Communication to the Göttingen Academy.- 3.6 Axioms of Hilbert’s Theory of Matter.- 3.7 Hilbert’s Fundamental Theorem, Energy Conservation and the World Function.- 4. Completion of the Theory of Gravitation.- 4.1 General Covariance and the Equivalence Principle.- 4.2 Theory of the Gravitational Field.- 4.3 Consequences and Applications of the Theory of Gravitation.- 4.4 The Cosmological Term.- 5. Physical Interpretation of General Covariance.- 5.1 Axiom of Physical Interpretability.- 5.2 Restrictions due to Causality.- 5.3 Hilbert’s Conclusion.- 6. Hamilton’s Principle and the Conservation Laws.- 6.1 Lorentz and the Hamilton Principle in Einstein’s Theory.- 6.2 Einstein and the Hamilton Principle.- 7. General Covariance and Conservation Laws.- 7.1 Energy Conservation and the Theory of Invariants.- 7.2 Identities from General Covariance.- 7.3 Bianchi Identities and Hilbert’s Constraint Conditions.- 8. Extension of General Relativity.- 8.1 Generalization of Riemannian Geometry.- 8.2 Weyl’s Unified Theory.- 8.3 Five-Dimensional Relativity.- 9. ‘Ein Bleibender Kern’ — An Enduring Core.- References and Notes.- Index of names.

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