Formulations of General Relativity Gravity Spinors and Differential Forms 1st Edition Kirill Krasnov 1108481647 9781108481649

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Product details:

• ISBN-10 ‏ : ‎ 1108481647
• ISBN-13 ‏ : ‎ 9781108481649
• Author: Kirill Krasnov

This monograph describes the different formulations of Einstein’s General Theory of Relativity. Unlike traditional treatments, Cartan’s geometry of fibre bundles and differential forms is placed at the forefront, and a detailed review of the relevant differential geometry is 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, and shown to lead to many practical simplifications. The book develops the chiral gravitational perturbation theory, in which the spinor formalism plays a central role. 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. Giving valuable insight into the very nature of gravity, this book joins our highly prestigious Cambridge Monographs in Mathematical Physics series. It will interest graduate students and researchers in the fields of theoretical physics and differential geometry.

Table of contents:

1 – Aspects of Differential Geometrypp 8-77

2 – Metric and Related Formulationspp 78-88

3 – Cartan’s Tetrad Formulationpp 89-124

4 – General Relativity in 2+1 Dimensionspp 125-131

5 – The ‘Chiral’ Formulation of General Relativitypp 132-191

6 – Chiral Pure Connection Formulationpp 192-249

7 – Deformations of General Relativitypp 250-254

8 – Perturbative Descriptions of Gravitypp 255-303

9 – Higher-Dimensional Descriptionspp 304-359

10 – Concluding Remarkspp 360-364

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