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,
divided in two volumes, is a rich resource for graduate students
and those who wish to gain a deep knowledge of the subject without
an instructor.
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 Fre is Professor of Theoretical Physics at the University
of Torino, Italy and is currently serving as Scientific Counsellor
of the Italian Embassy in Moscow. His scientific passion lies in
supergravity and all allied topics, since the inception of the
field, in 1976. He was professor at SISSA, worked in the USA and at
CERN. He has taught General Relativity for 15 years. He has
previously two scientific monographs, Supergravity and Superstrings
and The N=2 Wonderland, He is also the author of a popular science
book on cosmology and two novels, in Italian."
General
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