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A Relativist S Toolkit

Author: Eric Poisson
Publisher: Cambridge University Press
ISBN: 9781139451994
Size: 38.71 MB
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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.

Black Holes

Author: Sean Alan Hayward
Publisher: World Scientific
ISBN: 9814425702
Size: 43.59 MB
Format: PDF, Mobi
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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.

Cosmological And Black Hole Apparent Horizons

Author: Valerio Faraoni
Publisher: Springer
ISBN: 331919240X
Size: 43.90 MB
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This book overviews the extensive literature on apparent cosmological and black hole horizons. In theoretical gravity, dynamical situations such as gravitational collapse, black hole evaporation, and black holes interacting with non-trivial environments, as well as the attempts to model gravitational waves occurring in highly dynamical astrophysical processes, require that the concept of event horizon be generalized. Inequivalent notions of horizon abound in the technical literature and are discussed in this manuscript. The book begins with a quick review of basic material in the first one and a half chapters, establishing a unified notation. Chapter 2 reminds the reader of the basic tools used in the analysis of horizons and reviews the various definitions of horizons appearing in the literature. Cosmological horizons are the playground in which one should take baby steps in understanding horizon physics. Chapter 3 analyzes cosmological horizons, their proposed thermodynamics, and several coordinate systems. The remaining chapters discuss analytical solutions of the field equations of General Relativity, scalar-tensor, and f(R) gravity which exhibit time-varying apparent horizons and horizons which appear and/or disappear in pairs. An extensive bibliography enriches the volume. The intended audience is master and PhD level students and researchers in theoretical physics with knowledge of standard gravity.

Black Hole Physics

Author: V. Frolov
Publisher: Springer Science & Business Media
ISBN: 9780792351450
Size: 27.68 MB
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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.

Black Holes A Laboratory For Testing Strong Gravity

Author: Cosimo Bambi
Publisher: Springer
ISBN: 9811045240
Size: 23.10 MB
Format: PDF, ePub
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This textbook introduces the current astrophysical observations of black holes, and discusses the leading techniques to study the strong gravity region around these objects with electromagnetic radiation. More importantly, it provides the basic tools for writing an astrophysical code and testing the Kerr paradigm. Astrophysical black holes are an ideal laboratory for testing strong gravity. According to general relativity, the spacetime geometry around these objects should be well described by the Kerr solution. The electromagnetic radiation emitted by the gas in the inner part of the accretion disk can probe the metric of the strong gravity region and test the Kerr black hole hypothesis. With exercises and examples in each chapter, as well as calculations and analytical details in the appendix, the book is especially useful to the beginners or graduate students who are familiar with general relativity while they do not have any background in astronomy or astrophysics.“/p>

Geometry Topology And Physics Second Edition

Author: Mikio Nakahara
Publisher: CRC Press
ISBN: 9780750306065
Size: 77.50 MB
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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.