Underlying Mathematical Structures of Classical Gravitation Theory

  • Brandon Carter
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 44)


If I had been asked five years or so ago to prepare a course on recent developments in classical gravitation theory, I would not have hesitated in choosing the classical theory of black holes as a central topic of discussion. However the most important developments in gravitation theory during the last three or four years have not been in the classical domain at all but rather in the problems of quantisation of—or in—curved space-time. Associated with these developments (partly as a cause and partly as a consequence) has been a strong trend towards integration of gravitation theory with the main stream of theoretical physics, from which it had hitherto been rather isolated. The mahayana of this unification has been the generalised theory of gauge fields, which has made spectacular progress on the testing ground of weak interactions. Under these circumstances it seemed that instead of concentrating on the comparatively minor and specialised developments that have in fact recently taken place in the classical domain, it would be more appropriate for the present school to provide an introductory review of the general principles of classical gauge theory as a solid foundation underlying the more genuinely recent — and therefore quantum — developments to be described in subsequent courses.


Mathematical Structure Bianchi Identity Connection Form Parameter Subgroup Gravitation Theory 
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Copyright information

© Plenum Press, New York 1979

Authors and Affiliations

  • Brandon Carter
    • 1
  1. 1.Groupe d’Astrophysique RelativisteObservatoire de ParisMeudonFrance

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