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Author: Ovidiu Cristinel Stoica Publisher: Minkowski Institute Press ISBN: 9781927763346 Category : Languages : en Pages : 140
Book Description
This Thesis deals with recent progress regarding singularities in General Relativity. Singularities are predicted by the theory, but raise difficult problems, because they make the usual equations to be plagued with infinities and to break down. To resolve some of these problems, extensions of differential geometry and of Einstein's equation to singularities were needed, and were constructed by the author. This generalization works easily at the Big-Bang singularity, which gained by this a description in terms of finite quantities which have both geometric and physical meaning. Moreover, a large class of Big-Bang singularities which are not necessarily homogeneous or isotropic is presented. In addition, these singularities satisfy the Weyl curvature hypothesis, emitted by Penrose to explain the arrow of time. The black hole singularities apparently are more difficult to deal with, but by applying a special procedure they turn out as well to admit a description in terms of finite quantities. In addition, these singularities exhibit a (geo)metric dimensional reduction, which might act as a regulator for the quantum fields, including for quantum gravity, in the high-energy limit. This opens the perspective of perturbative quantum gravity without modifying General Relativity.
Author: Ovidiu Cristinel Stoica Publisher: Minkowski Institute Press ISBN: 9781927763346 Category : Languages : en Pages : 140
Book Description
This Thesis deals with recent progress regarding singularities in General Relativity. Singularities are predicted by the theory, but raise difficult problems, because they make the usual equations to be plagued with infinities and to break down. To resolve some of these problems, extensions of differential geometry and of Einstein's equation to singularities were needed, and were constructed by the author. This generalization works easily at the Big-Bang singularity, which gained by this a description in terms of finite quantities which have both geometric and physical meaning. Moreover, a large class of Big-Bang singularities which are not necessarily homogeneous or isotropic is presented. In addition, these singularities satisfy the Weyl curvature hypothesis, emitted by Penrose to explain the arrow of time. The black hole singularities apparently are more difficult to deal with, but by applying a special procedure they turn out as well to admit a description in terms of finite quantities. In addition, these singularities exhibit a (geo)metric dimensional reduction, which might act as a regulator for the quantum fields, including for quantum gravity, in the high-energy limit. This opens the perspective of perturbative quantum gravity without modifying General Relativity.
Author: D.N. Kupeli Publisher: Springer Science & Business Media ISBN: 9401587612 Category : Mathematics Languages : en Pages : 181
Book Description
This book is an exposition of "Singular Semi-Riemannian Geometry"- the study of a smooth manifold furnished with a degenerate (singular) metric tensor of arbitrary signature. The main topic of interest is those cases where the metric tensor is assumed to be nondegenerate. In the literature, manifolds with degenerate metric tensors have been studied extrinsically as degenerate submanifolds of semi Riemannian manifolds. One major aspect of this book is first to study the intrinsic structure of a manifold with a degenerate metric tensor and then to study it extrinsically by considering it as a degenerate submanifold of a semi-Riemannian manifold. This book is divided into three parts. Part I deals with singular semi Riemannian manifolds in four chapters. In Chapter I, the linear algebra of indefinite real inner product spaces is reviewed. In general, properties of certain geometric tensor fields are obtained purely from the algebraic point of view without referring to their geometric origin. Chapter II is devoted to a review of covariant derivative operators in real vector bundles. Chapter III is the main part of this book where, intrinsically, the Koszul connection is introduced and its curvature identities are obtained. In Chapter IV, an application of Chapter III is made to degenerate submanifolds of semi-Riemannian manifolds and Gauss, Codazzi and Ricci equations are obtained. Part II deals with singular Kahler manifolds in four chapters parallel to Part I.
Author: C Barrabès Publisher: World Scientific ISBN: 9814483370 Category : Science Languages : en Pages : 204
Book Description
' This book presents a comprehensive and self-contained exposition of the mathematical theory of impulsive light-like signals in general relativity. Applications are provided in relativistic astrophysics, cosmology and alternative theories of gravity deduced from string theory. Cataclysmic astrophysical events give rise to impulsive light-like signals which can generally be decomposed into a thin shell of null matter and an impulsive gravitational wave. Several examples are considered in black hole physics, wave collisions and light-like boosts of compact gravitating sources. Graduate students and researchers in relativistic astrophysics, cosmology and string theory will find this book very useful. Contents:General Description of an Impulsive Light-Like SignalIllustrations and Implications of the Bianchi IdentitiesLight-Like Boosts of Gravitating BodiesSpherically Symmetric Null ShellsCollisions of Plane Impulsive Light-Like SignalsImpulsive Light-Like Signals in Alternative Theories of Gravity Readership: Researchers, graduate students and upper-level undergraduates interested in general relativity. Keywords:General Relativity;Gravitational Waves;Light-Like Shells;Black Holes;CosmologyReviews:“For many years Barrabes and Hogan have been at the forefront of research on the physics and mathematics of singular lightlike hypersurfaces in general relativity. In this fine book they present their accumulated wisdom, for the benefit of students and researchers in this field. The book is dense with insight and beautiful results, and there is no doubt that the interested reader will indeed benefit greatly from this careful exposition.”Eric Poisson University of Guelph “… this book will stimulate the further development of models of impulsive and shock waves that are more closely related to cosmological and astrophysical processes.”Mathematical Reviews “This book is a very carefully prepared presentation about singular null hypersurfaces within General Relativity theory.”Zentralblatt MATH “The book is clearly written and all details of the calculations are supplied. To read it with profit requires a first course in general relativity at the final undergraduate or first year graduate student level, but is otherwise rather accessible. It can be recommended without reservation to anyone seriously interested in General Relativity and should be on the shelves of any physics or mathematics library. It is a major contribution to the subject and is likely to become a classic reference.”Contemporary Physics “The three fundamental papers which started this area of research all appeared at essentially the same time, 35 years ago; it is high time there was a unified presentation of the entire field. This book fills that need admirably, and could serve as the core of a graduate seminar for students having already taken a course in general relativity, or as a reference. My copy will have a treasured place in my library.”Classical and Quantum Gravity “I believe that the book is really useful both as an introduction to the field and as a reference for researchers … I think that ‘Singular Null Hypersurfaces’ is a really interesting book.”General Relativity and Gravitation “I believe that the book is really useful both as an introduction to the field and as a reference for researchers … it is a really interesting book.”Zentralblatt MATH '
Author: Roberto Mangabeira Unger Publisher: Cambridge University Press ISBN: 1107074061 Category : Science Languages : en Pages : 567
Book Description
Roberto Mangabeira Unger and Lee Smolin argue for a revolution in our cosmological ideas. Ideal for non-scientists, physicists and cosmologists.
Author: S. W. Hawking Publisher: Cambridge University Press ISBN: 1139810952 Category : Science Languages : en Pages :
Book Description
Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
Author: Bernard Schutz Publisher: Cambridge University Press ISBN: 0521887054 Category : Science Languages : en Pages : 411
Book Description
Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.
Author: Hubert Goenner Publisher: Springer Science & Business Media ISBN: 9780817640606 Category : Science Languages : en Pages : 678
Book Description
The past decade has seen a considerable surge of interest in historical and philo sophical studies of gravitation and relativity, due not only to the tremendous amount of world-wide research in general relativity and its theoretical and observational consequences, but also to an increasing awareness that a collaboration between working scientists, historians and philosophers of science is, in this field, partic ularly promising for all participants. The expanding activity in this field is well documented by recent volumes in this Einstein Studies series on the History of General Relativity as well as by a series of international conferences on this topic at Osgood Hill (1986), Luminy (1988), and Pittsburgh (1991). The fourth of these conferences, hosted by the Max Planck Institute for the History of Science, was held in Berlin from 31 July to 3 August 1995, with a record attendance of some 80 historians and philosophers of science, physicists, mathematicians, and as tronomers. Based on presentations at the Berlin conference, this volume provides an overview of the present state of research in this field, documenting not only the increasing scope of recent investigations in the history of relativity and gravitation but also the emergence of several key issues that will probably remain at the focus of debate in the near future. RELATIVITY IN THE MAKING The papers of this section deal with the origins and genesis of relativity theory.
Author: Ovidiu Cristinel Stoica
Author: Ovidiu Cristinel Stoica
Author: D.N. Kupeli
Author: C Barrabès
Author: W. Israel
Author: 
Author: Roberto Mangabeira Unger
Author: S. W. Hawking
Author: Bernard Schutz
Author: Robert Hermann
Author: Hubert Goenner