General Relativity: An Introduction to the Theory of the Gravitational Field

This book is an introduction to the theory of gravitation. It deals in an elementary way with those parts of the theory that are essential to the beginning student of general relativity, giving all the mathematics necessary to an understanding of the theory. Starting from the foundations of Riemannian geometry and the tensor calculus, the author formulates and works out the essential laws of physics in a Riemannian space. Next, the Einstein field equations are derived. All important applications of the theory are dealt with, including issues of current importance, in particular the Schwarzchild metric, gravitational waves, gravitational collapse, black holes and cosmological models. All the associated basic physical problems are fully discussed, but many results that draw heavily on mathematics are given without derivation. In the rather more demanding chapters on selected vector fields, groups of motion and the Petrov classification, methods are discussed which have proved to be especially fruitful in modern research.