Ebook: Introduction to General Relativity

In writing this text, our principal aim has been to show the close interaction of mathematical and physical ideas and to give the reader a feeling for the necessity and beauty of the laws of general relativity. We hope that our work will attract mathematicians to a fruitful and promising field of research which provides motivation and applications for many ideas and methods of modern analysis and differential geometry. At the same time we hope to provide the physicist with a simple and attractive introduction into powerful mathematical methods which may help him in various fields of theoretical research.

Since our main purpose in writing this book is frankly didactic, we have made a great effort to be clear and easily understood. We have tried to explain and motivate each "ansatz" even at the risk of being overly verbose and have carried out most calculations and transformations in great detail. We have preferred a lucid discussion of interesting special cases to a general and abstract formulation and have refrained from introducing mathematical concepts which may be very important in n-dimensional spaces with complex topology, but which do not have immediate applications to the physical theory considered.

Our restriction to the more elementary mathematical methods has also been motivated by the following consideration. The more elaborate the mathematical tools are, the more the future development of a physical
theory is predetermined and prejudged. It seems that the theory of gravitation and of general relativity is still far from completion and may progress-along lines yet unforeseen....