Formulations of General Relativity: Gravity, Spinors and Differential Forms (Cambridge Monographs on Mathematical Physics)

By: Kirill Krasnov

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Synopsis: This monograph carefully documents the different formulations of Einstein's general theory of relativity, and gives valuable insight into the very nature of gravity. Cartan's geometry of fibre bundles and differential forms are placed at the forefront, and a detailed review of the relevant differential geometry is also presented. Particular emphasis is given to general relativity in 4D space-time, in which the concepts of chirality and self-duality begin to play a key role. Associated chiral formulations are catalogued, allowing many practical simplifications. In addition to the chiral gravitational perturbation theory the book also presents in detail the twistor description of gravity, as well as its generalisation based on geometry of 3-forms in seven dimensions. Joining the highly prestigious Cambridge Monographs in Mathematical Physics series, this book will interest graduate students and researchers in the fields of general relativity and gravitational physics.