The Cosmological Singularity

Author: Vladimir Belinski,Marc Henneaux

Publisher: Cambridge University Press

ISBN: 1107047471

Category: Science

Page: 304

View: 1518

This book mathematically derives the theory underlying the Belinski-Khalatnikov-Lifshitz conjecture on the general solution of the Einstein equations with a cosmological singularity.
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Gravitational Collapse and Spacetime Singularities

Author: Pankaj S. Joshi

Publisher: Cambridge University Press

ISBN: 1139468146

Category: Science

Page: N.A

View: 9690

Physical phenomena in astrophysics and cosmology involve gravitational collapse in a fundamental way. The final fate of a massive star when it collapses under its own gravity at the end of its life cycle is one of the most important questions in gravitation theory and relativistic astrophysics, and is the foundation of black hole physics. General relativity predicts that continual gravitational collapse gives rise to a space-time singularity. Quantum gravity may take over in such regimes to resolve the classical space-time singularity. This book, first published in 2007, investigates these issues, and shows how the visible ultra-dense regions arise naturally and generically as an outcome of dynamical gravitational collapse. It will be of interest to graduate students and academic researchers in gravitation physics, fundamental physics, astrophysics, and cosmology. It includes a detailed review of research into gravitational collapse, and several examples of collapse models are investigated in detail.
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The Large Scale Structure of Space-Time

Author: S. W. Hawking,G. F. R. Ellis

Publisher: Cambridge University Press

ISBN: 1139810952

Category: Science

Page: N.A

View: 6232

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.
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Advanced General Relativity

Author: John Stewart

Publisher: Cambridge University Press

ISBN: 9780521449465

Category: Science

Page: 228

View: 4173

A self-contained introduction to advanced general relativity.
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Relativity on Curved Manifolds

Author: F. de Felice,C. J. S. Clarke

Publisher: Cambridge University Press

ISBN: 9780521429085

Category: Science

Page: 448

View: 4727

This is a self-contained exposition of general relativity with emphasis given to tetrad and spinor structures and physical measurement on curved manifolds.
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Spacetime and Singularities

An Introduction

Author: Gregory L. Naber

Publisher: Cambridge University Press

ISBN: 9780521336123

Category: Mathematics

Page: 178

View: 7101

Naber provides an elementary introduction to the geometrical methods and notions used in special and general relativity. Particular emphasis is placed on the ideas concerned with the structure of space-time and that play a role in the Penrose-Hawking singularity theorems. The author's primary purpose is to give a rigorous proof of the simplest of these theorems, by the one that is representative of the whole. He provides exercises and examples at the end of each chapter. No previous exposure either to relativity theory of differential geometry is required of the reader, as necessary concepts are developed when needed, though some restrictions ae imposed on the types of space considered.
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Exact Space-Times in Einstein's General Relativity

Author: Jerry B. Griffiths,Jiří Podolský

Publisher: Cambridge University Press

ISBN: 1139481169

Category: Science

Page: N.A

View: 7359

Einstein's theory of general relativity is a theory of gravity and, as in the earlier Newtonian theory, much can be learnt about the character of gravitation and its effects by investigating particular idealised examples. This book describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically. Concepts such as big bang and big crunch-types of singularities, different kinds of horizons and gravitational waves, are described in the context of the particular space-times in which they naturally arise. These notions are initially introduced using the most simple and symmetric cases. Various important coordinate forms of each solution are presented, thus enabling the global structure of the corresponding space-time and its other properties to be analysed. The book is an invaluable resource both for graduate students and academic researchers working in gravitational physics.
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Gravity and Strings

Author: Tomás Ortín

Publisher: Cambridge University Press

ISBN: 9780521035460

Category: Science

Page: 708

View: 7557

One appealing feature of string theory is that it provides a theory of quantum gravity. This volume is a self-contained, pedagogical exposition of this theory, its foundations and its basic results. Due to the large amount of background material, actions, solutions and bibliography contained within, this unique book can be used as a reference for research as well as a complementary textbook in graduate courses on gravity, supergravity and string theory.
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Differential Geometry, Gauge Theories, and Gravity

Author: M. Göckeler,T. Schücker

Publisher: Cambridge University Press

ISBN: 9780521378215

Category: Mathematics

Page: 230

View: 6176

Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.
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Supermanifolds

Author: Bryce DeWitt

Publisher: Cambridge University Press

ISBN: 9780521423779

Category: Science

Page: 407

View: 4046

This updated and expanded second edition of an established text presents a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the superanalogs of all the basic structures of ordinary manifold theory.
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Progress in String, Field and Particle Theory

Author: L. Baulieu,Eliezer Rabinovici,Jeff Harvey,Boris Pioline,Paul Windey

Publisher: Springer Science & Business Media

ISBN: 9401002118

Category: Science

Page: 509

View: 1730

The NATO Advanced Study Institute and EC Summer School "Progress in String Field and Particle Theory" was held in Cargse from June 25th till July 11th 2002. The main focus of the school was the recent progress in the very ac tive areas of superstring theory, quantum gravity and the theory of elementary particles. It covered topical problems in domains such as duality between gravity and gaugeinteractions, string field theory, tachyon condensation, non-commutative field theory, string cosmology and string phenomenology. The School featured daily introductory lectures and topical seminars. An informal Gong Show session allowed young post-doctoral researchers and senior graduate students to make a concise presentation oftheir current work. The School gave an excellent opportunity to the youngest researchers to establish a close relationship with their seniors and with the lecturers. These proceedings will further serve in fixing the acquired knowledge, and hopefully, become a useful reference for anyone working in this fascinating do main of physics. Some of the contributions provide an elementary introduction to their subject, while other ones are more geared to the specialist. We are deeply indebted to the NATO Division for Scientific Affairs for funding, and for their constant attention for our meetings, and to the European Commission for a High-Level Scientific Conference grant HPCFCT 2001-00298.
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Universal Themes of Bose-Einstein Condensation

Author: Nick P. Proukakis,David W. Snoke,Peter B. Littlewood

Publisher: Cambridge University Press

ISBN: 1107085691

Category: Science

Page: 697

View: 1207

Following an explosion of research on Bose-Einstein condensation (BEC) ignited by demonstration of the effect by 2001 Nobel prize winners Cornell, Wieman and Ketterle, this book surveys the field of BEC studies. Written by experts in the field, it focuses on Bose-Einstein condensation as a universal phenomenon, covering topics such as cold atoms, magnetic and optical condensates in solids, liquid helium and field theory. Summarising general theoretical concepts and the research to date - including novel experimental realisations in previously inaccessible systems and their theoretical interpretation - it is an excellent resource for researchers and students in theoretical and experimental physics who wish to learn of the general themes of BEC in different subfields.
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Scattering from Black Holes

Author: J. A. H. Futterman,F. A. Handler,Richard Alfred Matzner

Publisher: Cambridge University Press

ISBN: 0521329868

Category: Science

Page: 192

View: 6126

This book investigates the propagation of waves in the presence of black holes. Astrophysical black holes may eventually be probed by these techniques. The authors emphasise intuitive physical thinking in their treatment of the techniques of analysis of scattering, but alternate this with chapters on the rigourous mathematical development of the subject. High and low energy limiting cases are treated extensively and semi-classical results are also obtained. The analogy between Newtonian gravitational scattering and Coulomb quantum mechanical scattering is fully exploited. The book introduces the concepts of scattering by considering the simplest, scalar wave case of scattering by a spherical black hole. It then develops the formalism of spin-weighted spheroidal harmonics and of plane wave representations for neutrino, electromagnetic and gravitational scattering. Research workers and graduate and advanced undergraduate students in scattering theory, wave propagation and relativity will find this a comprehensive treatment of the topic.
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Techniques of Differential Topology in Relativity

Author: Roger Penrose

Publisher: SIAM

ISBN: 9781611970609

Category: Differential topology

Page: 72

View: 8347

Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.
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The Mathematical Theory of Black Holes

Author: Subrahmanyan Chandrasekhar

Publisher: Oxford University Press

ISBN: 9780198503705

Category: Science

Page: 646

View: 2670

"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.
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Ultracold Quantum Fields

Author: Henk T. C. Stoof,Dennis B. M. Dickerscheid,Koos Gubbels

Publisher: Springer Science & Business Media

ISBN: 1402087632

Category: Technology & Engineering

Page: 485

View: 4712

On June 19th 1999, the European Ministers of Education signed the Bologna Dec laration, with which they agreed that the European university education should be uniformized throughout Europe and based on the two cycle bachelor master’s sys tem. The Institute for Theoretical Physics at Utrecht University quickly responded to this new challenge and created an international master’s programme in Theoret ical Physics which started running in the summer of 2000. At present, the master’s programme is a so called prestige master at Utrecht University, and it aims at train ing motivated students to become sophisticated researchers in theoretical physics. The programme is built on the philosophy that modern theoretical physics is guided by universal principles that can be applied to any sub?eld of physics. As a result, the basis of the master’s programme consists of the obligatory courses Statistical Field Theory and Quantum Field Theory. These focus in particular on the general concepts of quantum ?eld theory, rather than on the wide variety of possible applica tions. These applications are left to optional courses that build upon the ?rm concep tual basis given in the obligatory courses. The subjects of these optional courses in clude, for instance, Strongly Correlated Electrons, Spintronics, Bose Einstein Con densation, The Standard Model, Cosmology, and String Theory.
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Quantum Gravity

Third Edition

Author: Claus Kiefer

Publisher: Oxford University Press

ISBN: 0199585202

Category: Mathematics

Page: 393

View: 2739

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".
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Euclidean Quantum Gravity

Author: G. W. Gibbons,Stephen W. Hawking

Publisher: World Scientific

ISBN: 9789810205164

Category: Science

Page: 586

View: 9969

The Euclidean approach to Quantum Gravity was initiated almost 15 years ago in an attempt to understand the difficulties raised by the spacetime singularities of classical general relativity which arise in the gravitational collapse of stars to form black holes and the entire universe in the Big Bang. An important motivation was to develop an approach capable of dealing with the nonlinear, non-perturbative aspects of quantum gravity due to topologically non-trivial spacetimes. There are important links with a Riemannian geometry. Since its inception the theory has been applied to a number of important physical problems including the thermodynamic properties of black holes, quantum cosmology and the problem of the cosmological constant. It is currently at the centre of a great deal of interest.This is a collection of survey lectures and reprints of some important lectures on the Euclidean approach to quantum gravity in which one expresses the Feynman path integral as a sum over Riemannian metrics. As well as papers on the basic formalism there are sections on Black Holes, Quantum Cosmology, Wormholes and Gravitational Instantons.
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A First Course in Loop Quantum Gravity

Author: Rodolfo Gambini,Jorge Pullin

Publisher: OUP Oxford

ISBN: 0191003239

Category: Science

Page: 192

View: 2930

This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.
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Moonshine beyond the Monster

The Bridge Connecting Algebra, Modular Forms and Physics

Author: Terry Gannon

Publisher: Cambridge University Press

ISBN: 9781139457804

Category: Science

Page: N.A

View: 2893

This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.
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