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General Relativity And The Einstein Equations

Author: Yvonne Choquet-Bruhat
Publisher: Oxford University Press
ISBN: 0199230722
Size: 41.39 MB
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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.

General Relativity And Gravitation

Author: Abhay Ashtekar
Publisher: Cambridge University Press
ISBN: 1316298698
Size: 52.38 MB
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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.

Geometric Analysis Around Scalar Curvatures

Author: Fei Han
Publisher: World Scientific
ISBN: 9813100567
Size: 46.32 MB
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This volume contains three expanded lecture notes from the program Scalar Curvature in Manifold Topology and Conformal Geometry that was held at the Institute for Mathematical Sciences from 1 November to 31 December 2014. The first chapter surveys the recent developments on the fourth-order equations with negative exponent from geometric points of view such as positive mass theorem and uniqueness results. The next chapter deals with the recent important progress on several conjectures such as the existence of non-flat smooth hyper-surfaces and Serrin's over-determined problem. And the final chapter induces a new technique to handle the equation with critical index and the sign change coefficient as well as the negative index term. These topics will be of interest to those studying conformal geometry and geometric partial differential equations. Contents:Lectures on the Fourth-Order Q Curvature Equation (Fengbo Hang and Paul C Yang)An Introduction to the Finite and Infinite Dimensional Reduction Methods (Manuel del Pino and Juncheng Wei)Einstein Constraint Equations on Riemannian Manifolds (Quôc Anh Ngô) Readership: Advanced undergraduates, graduate students and researchers interested in the study of conformal geometry and geometric partial differential equations.

Colliding Plane Waves In General Relativity

Author: Jeremy Bransom Griffiths
Publisher: Oxford University Press, USA
ISBN: 9780198532095
Size: 23.70 MB
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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 Mathematical Theory Of Black Holes

Author: Subrahmanyan Chandrasekhar
Publisher: Oxford University Press
ISBN: 9780198503705
Size: 28.37 MB
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"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.

A Century Of Relativity Physics

Author: Lysiane Mornas
ISBN: 9780735403338
Size: 14.69 MB
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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.

Advanced General Relativity

Author: Claude Barrabès
Publisher: OUP Oxford
ISBN: 0199680698
Size: 45.78 MB
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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 Topology And Future Stability Of The Universe

Author: Hans Ringström
Publisher: OUP Oxford
ISBN: 0199680299
Size: 38.16 MB
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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.