Volume 1: Development of the Theory and Basic Physical Applications
Frè, Pietro Giuseppe
2013, XVIII, 338 p.
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Presents general relativity not in isolation, but as a cornerstone of modern theoretical physics
Gives a systematic exposition of the theory in a self-contained but rigorous mathematical language and includes complete analytical studies of some relevant proplems
Covers both classical general relativity and supergravity
Offers plenty of historical background on the physicists relevant to the theories presented
Enriched with useful appendices with material on spinors, Mathematica programmes, and much more
‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes.
Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differentiable manifolds, fibre-bundles, differential forms, and the theory of connections are covered, with a sketchy introduction to homology and cohomology. (Pseudo)-Riemannian geometry is presented both in the metric and in the vielbein approach. Physical applications include the motions in a Schwarzschild field leading to the classical tests of GR (light-ray bending and periastron advance) discussion of relativistic stellar equilibrium, white dwarfs, Chandrasekhar mass limit and polytropes. An entire chapter is devoted to tests of GR and to the indirect evidence of gravitational wave emission. The formal structure of gravitational theory is at all stages compared with that of non gravitational gauge theories, as a preparation to its modern extension, namely supergravity, discussed in the second volume.
Pietro Frè is Professor of Theoretical Physics at the University of Torino, Italy. He has taught General Relativity for 15 years.
Content Level »Graduate
Keywords »Black Holes - Cosmological and Astrophysical Applications of GR - Gauge Theory - Gravitational Waves - Mathematical and Geometrical Foundations of General relativity - Supergravity and Supestring Theory - Textbook on General Relativity