General Relativity and the Einstein Equations (Oxford Mathematical Monographs) - Tapa dura

The book is a refreshing exposition of what is not known: The reader will come away feeling that general relativity has many exciting aspects to it just waiting to be discovered. (Physics Today)

General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.