Formulations of General Relativity: Gravity, Spinors and Differential Forms

Kirill Krasnov

doi:10.1017/9781108674652

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.

‘The work is mathematically rigorous and complete. Researchers working in fields such as quantum gravity will find this a very useful reference. Postgraduate students will also find it a helpful adjunct to the usual books on general relativity.’

Source: Choice

'… in this book Krasnov deals mainly with chiral formulations of four-dimensional general relativity, a topic that usually is not present in most (if not all) of the relevant textbooks, thereby bringing to the forefront the importance of Cartan’s calculus of differential forms, the geometry of fibre bundles, but also spinors and (finally) twistors.'

Theophanes Grammenos Source: MathSciNet

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Formulations of General Relativity

Gravity, Spinors and Differential Forms

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Contents

Frontmatter
pp i-vi

Dedication
pp vii-viii

Contents
pp ix-xii

Preface
pp xiii-xviii

Introduction
pp 1-7

1 - Aspects of Differential Geometry
pp 8-77

2 - Metric and Related Formulations
pp 78-88

3 - Cartan’s Tetrad Formulation
pp 89-124

4 - General Relativity in 2+1 Dimensions
pp 125-131

5 - The ‘Chiral’ Formulation of General Relativity
pp 132-191

6 - Chiral Pure Connection Formulation
pp 192-249

7 - Deformations of General Relativity
pp 250-254

8 - Perturbative Descriptions of Gravity
pp 255-303

9 - Higher-Dimensional Descriptions
pp 304-359

10 - Concluding Remarks
pp 360-364

References
pp 365-368

Index
pp 369-372

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Formulations of General Relativity

Gravity, Spinors and Differential Forms

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