Relativity And Gravitation

Physics and mathematics students are as eager as ever to become acquainted withthefoundationsofgeneralrelativityandsomeofitsmajorapplicationsin astrophysics and cosmology. I hope that this textbook gives a comprehensive and timelyintroduction toboth aspectsof thisfascinating?eld,and willturn out to be useful for undergraduate and graduate students. This book is a complete revision and extension of my previous volume ‘GeneralRelativityandRelativisticAstrophysics’thatappearedabouttwenty years ago in the Springer Series‘Texts and Monographs in Physics’; however, it cannot be regarded just as a new edition. In Part I the foundations of general relativity are thoroughly developed. Some of the more advanced topics, such as the section on the initial value problem, can be skipped in a ?rst reading. Part II is devoted to tests of general relativity and many of its app- cations. Binary pulsars – our best laboratories for general relativity – are studied in considerable detail. I have included an introduction to gravi- tional lensing theory, to the extend that the current literature on the subject should become accessible. Much space is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel’s proof of his uniqueness theorem, and a derivation of the basic laws of black hole physics. Part II ends with Witten’s proof of the positive energy theorem. All the required di?erential geometric tools are developed in Part III.

In the early 1900s, Albert Einstein formulated two theories that would forever change the landscape of physics: the Special Theory of Relativity and the General Theory of Relativity. By 1925, quantum mechanics had been born out of the dissection of these two theories, and shortly after that, relativistic quantum field theory. We now had in place some important ties between the laws of physics and the types of particle interactions the new physics was uncovering.

The transition from classical to modern physics in the ?rst half of the twentieth c- tury by quantum and relativity theories affected some of the most fundamental notions of physical thinking, such as matter, radiation, space, and time. This tran- tion thus represents a challenge for any attempt to understand the structures of a s- enti?c revolution. The present four-volume work aims at a comprehensive account of the way in which the work of Albert Einstein and his contemporaries changed our understanding of space, time, and gravitation. The conceptual framework of classical nineteenth-century physics had to be fundamentally restructured and reinterpreted in order to arrive at a theory of gravitation compatible with the new notions of space and time established in 1905 by Einstein’s special theory of relativity. Whereas the classical theory of gravitation postulated an instantaneous action at a distance, Einstein’s new relativistic kinematics rather suggested an analogy between the gravitational ?eld and the electromagnetic ?eld, propagating with a ?nite speed. It is therefore not surprising that Einstein was not alone in addressing the problem of formulating a theory of gravitation that complies with the kinematics of relativity t- ory. The analysis of these alternative approaches, as well as of earlier alternative approaches to gravitation within classical physics, turns out to be crucial for identi- ing the necessities and contingencies in the actual historical development.

This work presents gravitation and gauge fields as interrelated topics with a common physical and mathematical foundation, such as gauge theory of gravitation and other fields, giving emphasis to the physicist's point of view.