Krasnov K. Formulations of General Relativity: Gravity, Spinors and Differential Forms

Cambridge University Press, 2020. — 391 p. — (Cambridge Monographs on Mathematical Physics). — ISBN: 978-1-108-48164-9.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.Aspects of Differential Geometry
Metric and Related Formulations
Cartan’s Tetrad Formulation
General Relativity in 2+1 Dimensions
The ‘Chiral’ Formulation of General Relativity
Chiral Pure Connection Formulation
Deformations of General Relativity
Perturbative Descriptions of Gravity
Higher-Dimensional Descriptions