Einstein's General Theory of Relativity: With Modern Applications in Cosmology [Hardcover]

The book introduces the general theory of relativity and includes applications to cosmology.  The book contains a thorough introduction to tensor calculus and curved manifolds.  After the necessary mathematical tools are introduced, we give a thorough presentation of the theory of relativity.  Also, some advanced topics not previously covered by textbooks; e.g. Kaluza-Klein theory, Israel's formalism and branes.  Anisotropic cosmological models are also included.

The book contains a large number of new exercises and examples, each with separate headings.  The reader will get an updated introduction to general relativity including the most recent developments in cosmology.

Introduction: Newtonian Physics And Special Relativity.- Relativity Principles and Gravitation.- The Special Theory of Relativity.- The Mathematics Of The General Theory Of Relativity.- Vectors, Tensors, and Forms.- Basis Vector Fields and the Metric Tensor.- Non-inertial Reference Frames.- Differentiation, Connections, and Integration.- Curvature.- Einstein's Field Equations.- Einstein's Field Equations.- The Linear Field Approximation.- The Schwarzschild Solution and Black Holes.- Cosmology.- Homogeneous and Isotropic Universe Models.- Universe Models with Vacuum Energy.- Anisotropic and Inhomogeneous Universe Models.- Advanced Topics.- Covariant Decomposition, Singularities, and Canonical Cosmology.- Spatially Homogeneous Universe Models.- Israel's Formalism: The Metric Junction Method.- Brane-worlds.- Kaluza-Klein Theory.

From the reviews:

A sophisticated treatment of general relativity with a considerable number of applications to cosmology. & The book may be read in several different ways, depending on the interests of readers. A rich source of material; college libraries should have it on their shelves. Summing Up: Highly recommended. Upper-division undergraduates thls.