London Mathematical Society Student Texts
2 total works
This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. The choice of material presented has evolved from graduate courses given in London and Oxford and the authors have aimed to retain the informal tone of those lectures. Topics covered include spinor algebra andcalculus; compactified Minkowski space; the geometry of null congruences; the geometry of twistor space; an informal account of sheaf cohomology sufficient to describe the twistor solution for the zero rest-mass equations; the active twistor constructions which solve the self-dual Yang-Mills and Einstein equations; and Penrose's quasi- local-mass construction. Exercises are included in the text and after most chapters. The book will provide graduate students with an introduction to the literature of twistor theory, presupposing some knowledge of special relativity and differential geometry. It would also be of use for a short course on space-time structure independent of twistor theory.
This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.