**Author**: Yvonne Choquet-Bruhat

**Publisher:** Oxford University Press

**ISBN:** 0199230722

**Category:** Mathematics

**Page:** 785

**View:** 4216

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.

Explore spectacular advances in cosmology, relativistic astrophysics, gravitational wave science, mathematics, computational science, and the interface of gravitation and quantum physics with this unique celebration of the centennial of Einstein's discovery of general relativity. Twelve comprehensive and in-depth reviews, written by a team of world-leading international experts, together present an up-to-date overview of key topics at the frontiers of these areas, with particular emphasis on the significant developments of the last three decades. Interconnections with other fields of research are also highlighted, making this an invaluable resource for both new and experienced researchers. Commissioned by the International Society on General Relativity and Gravitation, and including accessible introductions to cutting-edge topics, ample references to original research papers, and informative colour figures, this is a definitive reference for researchers and graduate students in cosmology, relativity, and gravitational science.

The papers in this volume cover a wide variety of topics in differential geometry, general relativity, and partial differential equations. In addition, there are several articles dealing with various aspects of Lie groups and mathematics physics. Taken together, the articles provide the reader with a panorama of activity in general relativity and partial differential equations, drawn by a number of leading figures in the field. The companion volume (Contemporary Mathematics, Volume 553) is devoted to function theory and optimization.

"The theory of black holes is the most simple consequence of Einstein's relativity theory. Dealing with relativity theory, this book details one of the most beautiful areas of mathematical physics; the theory of black holes. It represents a personal testament to the work of the author, who spent several years working-out the subject matter." --WorldCat.

The collision and non-linear interaction of plane waves in Einstein's general theory of relativity has received considerable attention in recent years. Initially, it was widely thought that such collisions inevitable produce curvature singularities. More recently, however, a surprisingly rich structure of such space-times has been discovered. This volume presents a unified and comprehensive survey to the current research in this topic which will be suitable for graduate students and research workers whose research lies in general relativity. The first eight chapters present the background to the subject, introduce the field equations, and include a discussion of some qualitative aspects of their solution. A detailed account is included of the Kahn-Penrose solution since it exhibits the general character of most colliding plane wave solutions. The latter half of the book is devoted to a catalogue of further exact solutions describing the collision of both gravitational and electromagnetic plane waves. This includes a discussion of the significance of known solutions and a summary of topics of current research interest. As a result, the book will serve both as an invaluable research reference and also as the means to teach and study this active area of research in general relativity.

The book covers mainstream topics at research level involving gravitational waves, spinning particles, and black holes, suitable for graduates and early postgraduates exploring avenues into research in general relativity.

On the occasion of the World Year of Physics, which commemorated the centenary of the publication of several major papers by Einstein and the birth of the Theory of Relativity, this edition of the Spanish Relativity Meeting endeavored to cover as many aspects as possible of the foundations, applications and future vistas of this branch of modern physics. Topics included are: foundations of special and general relativity, observational tests, relativistic astrophysics, gravitational waves, numerical relativity, cosmology, early universe, dark matter, exact solutions of Einstein equations, black holes, quantum gravity, string theory, discrete space-time, non-commutative geometry, relativistic statistical and nuclear physics, compact stars, and historical and philosophical perspectives.

This 1973 book discusses Einstein's General Theory of Relativity and its predictions concerning black holes and singularities in space-time itself.

A general introduction to the initial value problem for Einstein's equations coupled to collisionless matter. The book contains a proof of future stability of models of the universe consistent with the current observational data and a discussion of the restrictions on the possible shapes of the universe imposed by observations.

Edgard Gunzig and Pasquale Nardone RGGR Universite Libre de Bruxelles CP231 1050 Bruxelles Belgium The NATO Advanced Research Workshop on "The Origin of Structure in the Universe" was organized to bring together workers in various aspects of relativistic cosmology with the aim of assessing the present status of our knowledge on the formation and evolution of structure. As it happened, the meeting was particularly timely. Only two days before the 30 or so physicists from many countries gathered for a week at the Chateau du Pont d'Oye, in the forests of the southern Belgian province of Luxembourg, newspaper headlines all over the world announced the results of the analysis of the first full year of data from the Cosmic Background Observer Satellite (COBE). This long-awaited confirmation of the theoretically predicted anisotropy in the microwave background radiation opened a new era in observational cos mology. The realization of the new relevance of the subject of the workshop and the questions raised by the observational results, in addition to bring ing TV crews and newspaper journalists, naturally influenced and stimulated many discussions among the participants. The success of the meeting as usual is due to a combination of factors. Besides the high quality of the talks, discussions were encouraged by the warm atmosphere of the Chateau, for which we are grateful to Mme. Camille Orts, and its beautiful surroundings, not to mention the marvelous cuisine.

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking.

Quantum theory and Einstein's theory of relativity are at the centre of modern theoretical physics, yet, the consistent unification of both theories is still elusive. This book offers an up-to-date introduction into the attempts to construct a unified theory of "quantum gravity".

'An excellent and self-contained treatment of the mathematical theory of hyperbolic systems of conservation laws... written in a clear and self-contained way and will be of great value for graduate students and specialists in the field.' -EMSHyperbolic systems of partial differential equations are important in modelling various physical systems, in particular the development of shock waves in fluids. As such they find many applications in areas of engineering and aerospace research. This book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions characterized by the appearance of shock waves. It is the first monograph on the subject which gives a detailed description of the front tracking algorithm, and a comprehensive account of the new, fundamental results on the uniqueness and stability of solutions.

This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.

Keine wissenschaftliche Theorie ist auf solche Faszination auch außerhalb der Wissenschaft gestoßen wie die Allgemeine Relativitätstheorie von Albert Einstein, und keine wurde so nachdrücklich mit den Mitteln der modernen Physik überprüft. Wie hat sie diesen Test mit Raumsonden, Radioastronomie, Atomuhren und Supercomputern standgehalten? Hatte Einstein recht? Mit der Autorität des Fachmanns und dem Flair des unvoreingenommenen Erzählers schildert Clifford Will die Menschen, Ideen und Maschinen hinter den Tests der allgemeinen Relativitätstheorie. Ohne Formeln und Fachjargon wird der leser mit Einsteins Gedanken vertraut und erfährt von der Bestätigung seiner Vorhersagen, angefangen bei der Lichtablenkung im Schwerefeld der Sonne 1919 bis zu den ausgefeilten Kreiselexperimenten auf dem Space Shuttle. Die Allgemeine Relativitätstheorie hat nich nur alle diese Tests bestanden, sie hat darüber hinaus wesentlich beigetragen zu unserem Verständnis von Phänomenen wie Pulsaren, Quasaren, Schwarzen Löchern und Gravitationslinsen. Dieses Buch erzählt lebendig und spannend die Geschichte einer der größten geistigen Leistungen unserer Zeit.