A Relativist's Toolkit

The Mathematics of Black-Hole Mechanics

Author: Eric Poisson

Publisher: Cambridge University Press

ISBN: 9781139451994

Category: Science

Page: N.A

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This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.
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Black Hole Physics

Basic Concepts and New Developments

Author: V. Frolov,I. Novikov

Publisher: Springer Science & Business Media

ISBN: 9780792351450

Category: Science

Page: 770

View: 7954

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This volume on black holes can be seen as a sequel to Physics of Black Holes, published by Kluwer Academic Publishers in 1989. The authors are recognised experts in their field, and have many years' experience in teaching courses on general relativity and black holes. The present work covers practically all aspects of black hole physics and its astrophysical applications. Among the topics treated in depth are: spacetime of stationary black holes, general theory of black holes, black hole perturbations, black hole numerics, black hole electrodynamics, black holes in unified theories of gravity, quantum black holes, final states of evaporating black holes and the information loss puzzle. Special attention is paid to the role of black holes in astrophysics and observational evidence of black hole existence. Many exotic subjects linked with black holes, such as white holes, wormholes, and time machines are discussed in detail. Numerous appendices cover mathematical aspects of general relativity and black holes and quantum field theory in curved space time. This makes the book practically self-contained. Extensive references provide the reader with a guide to the literature in this field. Audience: This book will be of interest to researchers and postgraduate students whose work involves relativity and gravitation, statistical physics, thermodynamics, active galactic nuclei and stellar physics.
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Einstein Equations: Physical and Mathematical Aspects of General Relativity

Domoschool 2018

Author: Sergio Cacciatori,Batu Güneysu,Stefano Pigola

Publisher: Springer Nature

ISBN: 3030180611

Category: Science

Page: 357

View: 4458

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This book is based on lectures given at the first edition of the Domoschool, the International Alpine School in Mathematics and Physics, held in Domodossola, Italy, in July 2018. It is divided into two parts. Part I consists of four sets of lecture notes. These are extended versions of lectures given at the Domoschool, written by well-known experts in mathematics and physics related to General Relativity. Part II collects talks by selected participants, focusing on research related to General Relativity.
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Introduction to Black Hole Physics

Author: Valeri P. Frolov,Andrei Zelnikov

Publisher: OUP Oxford

ISBN: 0191003220

Category: Science

Page: 506

View: 777

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This book is about black holes, one of the most intriguing objects of modern theoretical physics and astrophysics. For many years, black holes have been considered as interesting solutions of the Theory of General Relativity with a number of amusing mathematical properties. Now after the discovery of astrophysical black holes, the Einstein gravity has become an important tool for their study. This self-contained textbook combines physical, mathematical, and astrophysical aspects of black hole theory. Pedagogically presented, it contains 'standard' material on black holes as well as relatively new subjects such as the role of hidden symmetries in black hole physics, and black holes in spacetimes with large extra dimensions. The book will appeal to students and young scientists interested in the theory of black holes.
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Black Holes

New Horizons

Author: Sean Alan Hayward

Publisher: World Scientific

ISBN: 9814425702

Category: Science

Page: 280

View: 6896

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Black holes, once just fascinating theoretical predictions of how gravity warps space-time according to Einstein's theory, are now generally accepted as astrophysical realities, formed by post-supernova collapse, or as supermassive black holes mysteriously found at the cores of most galaxies, powering active galactic nuclei, the most powerful objects in the universe. Theoretical understanding has progressed in recent decades with a wider realization that local concepts should characterize black holes, rather than the global concepts found in textbooks. In particular, notions such as trapping horizon allow physically meaningful quantities and equations, describing how a black hole evolves. This has led to discoveries in fields as diverse as classical and numerical general relativity, differential geometry, thermodynamics, quantum field theory, and quantum gravity. There is heretofore no one volume which covers all the main aspects, so this volume collects together summaries and recent research, each chapter written by an expert or experts in a given field. This is intended for readers at a graduate level upwards, who wish to learn about the wide range of research concerning black holes.
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Geometry, Topology and Physics, Second Edition

Author: Mikio Nakahara

Publisher: CRC Press

ISBN: 9780750306065

Category: Mathematics

Page: 596

View: 1056

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Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
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Theory

Author: Sergei M. Kopeikin

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110337495

Category: Science

Page: 366

View: 7806

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Relativistic celestial mechanics – investigating the motion celestial bodies under the influence of general relativity – is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics – starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area. This first volume of a two-volume series is concerned with theoretical foundations such as post-Newtonian solutions to the two-body problem, light propagation through time-dependent gravitational fields, as well as cosmological effects on the movement of bodies in the solar systems. On the occasion of his 80-th birthday, these two volumes honor V. A. Brumberg – one of the pioneers in modern relativistic celestial mechanics. Contributions include: M. Soffel: On the DSX-framework T. Damour: The general relativistic two body problem G. Schaefer: Hamiltonian dynamics of spinning compact binaries through high post-Newtonian approximations A. Petrov and S. Kopeikin: Post-Newtonian approximations in cosmology T. Futamase: On the backreaction problem in cosmology Y. Xie and S. Kopeikin: Covariant theory of the post-Newtonian equations of motion of extended bodies S. Kopeikin and P. Korobkov: General relativistic theory of light propagation in multipolar gravitational fields
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General Relativity

Author: Norbert Straumann

Publisher: Springer Science & Business Media

ISBN: 9400754094

Category: Science

Page: 736

View: 1561

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This book provides a completely revised and expanded version of the previous classic edition ‘General Relativity and Relativistic Astrophysics’. In Part I the foundations of general relativity are thoroughly developed, while Part II is devoted to tests of general relativity and many of its applications. Binary pulsars – our best laboratories for general relativity – are studied in considerable detail. An introduction to gravitational lensing theory is included as well, so as to make the current literature on the subject accessible to readers. Considerable attention is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel’s proof of his uniqueness theorem, and a derivation of the basic laws of black hole physics. Part II ends with Witten’s proof of the positive energy theorem, which is presented in detail, together with the required tools on spin structures and spinor analysis. In Part III, all of the differential geometric tools required are developed in detail. A great deal of effort went into refining and improving the text for the new edition. New material has been added, including a chapter on cosmology. The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It utilizes a very well structured approach, which should help it continue to be a standard work for a modern treatment of gravitational physics. The clear presentation of differential geometry also makes it useful for work on string theory and other fields of physics, classical as well as quantum.
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