The Mathematical Theory of Relativity
by Arthur Stanley Eddington
Publisher: Cambridge University Press 1923
Number of pages: 448
Sir Arthur Eddington here formulates mathematically his conception of the world of physics derived from the theory of relativity. The argument is developed in a form which throws light on the origin and significance of the great laws of physics; its consequences are followed to the full extent in the consideration of gravitation, relativity, mechanics, space-time, electromagnetic phenomena and world geometry.
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by Neil Lambert - King's College London
Contents: Introduction; Manifolds and Tensors; General Relativity (Derivation, Diffeomorphisms as Gauge Symmetries, Weak Field Limit, Tidal Forces, ...); The Schwarzchild Black Hole; More Black Holes; Non-asymptotically Flat Solutions.
by Sean M. Carroll - University of California
Lecture notes on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology.
by Bernard F Schutz, Franco Ricci - arXiv
Notes of lectures for graduate students, covering the theory of linearized gravitational waves, their sources, and the prospects at the time for detecting gravitational waves. The lectures remain of interest for pedagogical reasons.
by Gerard 't Hooft - Utrecht University
Contents: The Metric of Space and Time; Curved coordinates; A short introduction to General Relativity; Gravity; The Schwarzschild Solution; The Chandrasekhar Limit; Gravitational Collapse; The Reissner-Nordstrom Solution; Horizons; and more.