Formulations of General Relativity
Gravity, Spinors and Differential Forms

Documenting the different formulations of general relativity, this book reveals valuable insight into the nature of the gravitational force.

Kirill Krasnov (Author)

9781108481649, Cambridge University Press

Hardback, published 26 November 2020

404 pages, 5 b/w illus. 1 table
17.3 x 25 x 2.5 cm, 0.82 kg

'… 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, MathSciNet

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.

Preface
Introduction
1. Aspects of differential geometry
2. Metric and related formulations
3. Cartan's tetrad formulation
4. General relativity in 2+1 dimensions
5. The 'chiral' formulation of general relativity
6. Chiral pure connection formulation
7. Deformations of general relativity
8. Perturbative descriptions of gravity
9. Higher-dimensional descriptions
10. Concluding remarks
References
Index.

Subject Areas: Mathematical physics [PHU], Relativity physics [PHR], Gravity [PHDV], Cosmology & the universe [PGK]