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General relativity today. (English) Zbl 1142.83002
Damour, Thibault (ed.) et al., Gravitation and experiment. Poincaré Seminar 2006. Papers of the seminar, Paris, France, October 28, 2006. Basel: Birkhäuser (ISBN 978-3-7643-8523-1/hbk). Progress in Mathematical Physics 52, 1-49 (2007).
General Theory of Relativity (GTR) is essentially a single exceptionally brilliant mind’s contribution. Albert Einstein can, indeed, be considered as one of the most outstanding intellects of the last century for many of his great achievements of which GTR stands perhaps at the top.
In this 49-page quite interesting paper the author has after recalling conceptual foundations and the basic structure of GTR, reviewed certain chief modern developments including some aspects of cosmology. Historical progress of the field is touched upon in the introduction, followed by a brief discussion on special relativity, principle of equivalence, gravitation and space-time-chronogeometry, Einstein’s equations: Elastic space-time, weak-field limit and Newtonian limit, post-Newtonian approximation, strong gravitational fields and black-holes, binary pulsars, gravitational waves etc. The connections between GTR and quantum theory from supergravity to modern string theory are discussed at length. Max Born’s admiring comment about “The marvelous intellectual construction of GTR – the greatest feat of human thought concerning nature, the most outstanding association of philosophical penetration, physical intuition and mathematical ability – to be appreciated from a distance” is quoted. GTR’s primary role in large domains of physics inclusive of internal atomic time and quantum geometry and other aspects of modern physics is stressed.
In this extensive work on GTR we have a very good coverage of this important subject.
For the entire collection see [Zbl 1124.83004].

83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83A05 Special relativity
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C57 Black holes
83C35 Gravitational waves