|Advanced General Relativity||
General relativity is one of the cornerstones of modern physics, describing gravitational phenomena in geometric manner. Advanced General Relativity by John Stewart provides an introduction to some of the more advanced mathematical aspects of the theory. The readership is graduate students and researchers who already have some knowledge of general relativity.
Chapter 1 outlines the theory of differential manifolds, the tangent and cotangent spaces, tensor algebra, Lie derivatives, connections, geodesics and curvature tensors. All these geometric ideas are the “bread and butter” of general relativity.
Chapter 2 is where the more advanced topics start. The notion of spinors is introduced here. The Petrov classification and the Newman-Penrose formulation are presented.
Chapter 3 deals with asymptotic properties of space-time. Basically one would expect the space-time far away from an isolated source of gravity to be flat. This chapter deals with the Bondi and ADM mass, asymtopia for Minkowski space-time, asymptotic simplicity and conformal transformations.
Chapter 4 deals with the characteristic initial value problem in general relativity. The idea is to reformulate general relativity as the temporal evolution of 3-spaces.
Two appendices are included. The first deals with Dirac spinors and the second with the Newman-Penrose formalism.
Paperback: 240 pages
Publisher: Cambridge University Press; New Ed edition (26 Nov 1993)