Formulations of General Relativity: Gravity, Spinors and Differential Forms

ISBN-13: 9781108481649 / Angielski / Twarda / 2020 / 404 str.

Kirill Krasnov (University of Nottingham)

Opis

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.

Recenzje

'… 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

Spis treści

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.