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The Geometry of Kerr Black Holes

The Geometry of Kerr Black Holes Author Barrett O'Neill
ISBN-10 9780486783116
Release 2014-01-15
Pages 400
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Suitable for advanced undergraduates and graduate students of mathematics as well as for physicists, this unique monograph and self-contained treatment constitutes an introduction to modern techniques in differential geometry. 1995 edition.

The Mathematical Theory of Black Holes

The Mathematical Theory of Black Holes Author Subrahmanyan Chandrasekhar
ISBN-10 0198503709
Release 1998-01-01
Pages 646
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Part of the reissued Oxford Classic Texts in the Physical Sciences series, this book was first published in 1983, and has swiftly become one of the great modern classics of relativity theory. It represents a personal testament to the work of the author, who spent several years writing and working-out the entire subject matter. The theory of black holes is the most simple and beautiful consequence of Einstein's relativity theory. At the time of writing there was no physical evidence for the existence of these objects, therefore all that Professor Chandrasekhar used for their construction were modern mathematical concepts of space and time. Since that time a growing body of evidence has pointed to the truth of Professor Chandrasekhar's findings, and the wisdom contained in this book has become fully evident.

Curvature in Mathematics and Physics

Curvature in Mathematics and Physics Author Shlomo Sternberg
ISBN-10 9780486292717
Release 2013-04-17
Pages 416
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Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Black Holes in Higher Dimensions

Black Holes in Higher Dimensions Author Gary T. Horowitz
ISBN-10 9781107013452
Release 2012-04-19
Pages 422
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"Black holes are one of the most remarkable predictions of Einstein's general relativity. Now widely accepted by the scientific community, most work has focussed on black holes in our familiar four spacetime dimensions. But in recent years, ideas in brane-world cosmology, string theory, and gauge/gravity duality have all motivated a study of black holes in more than four dimensions, with surprising results. In higher dimensions, black holes exist with exotic shapes and unusual dynamics. Edited by leadingexpert Gary Horowitz, this exciting book is the first devoted to this new field. The major discoveries are explained by the people who made them: RobMyers describes theMyers-Perry solutions that represent rotating black holes in higher dimensions; Ruth Gregory describes the Gregory-Laflamme instability of black strings; and Juan Maldacena introduces gauge/gravity duality, the remarkable correspondence that relates a gravitational theory to nongravitational physics. There are two additional chapters on this duality describing how black holes can be used to describe relativistic fluids and aspects of condensed matter physics"--

Semi Riemannian Geometry With Applications to Relativity

Semi Riemannian Geometry With Applications to Relativity Author Barrett O'Neill
ISBN-10 0080570577
Release 1983-07-29
Pages 468
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This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.

Black Holes

Black Holes Author Derek J. Raine
ISBN-10 9781848163829
Release 2010
Pages 198
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This introduction to the fascinating subject of black holes fills a significant gap in the literature which exists between popular, non-mathematical expositions and advanced textbooks at the research level. It is designed for advanced undergraduates and first year postgraduates as a useful stepping-stone to the advanced literature. The book provides an accessible introduction to the exact solutions of Einstein's vacuum field equations describing spherical and axisymmetric (rotating) black holes. The geometry and physical properties of these spacetimes are explored through the motion of particles and light. The use of different coordinate systems, maximal extensions and Penrose diagrams is explained. The association of the surface area of a black hole with its entropy is discussed and it is shown that with the introduction of quantum mechanics black holes cease to be black and can radiate. This result allows black holes to satisfy the laws of thermodynamics and thus be consistent with the rest of physics. In this new edition the problems in each chapter have been revised and solutions are provided. The text has been expanded to include new material on wormholes and clarify various other issues.

Elementary Differential Geometry

Elementary Differential Geometry Author Barrett O'Neill
ISBN-10 9781483268118
Release 2014-05-12
Pages 422
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Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.

The Future of Theoretical Physics and Cosmology

The Future of Theoretical Physics and Cosmology Author G. W. Gibbons
ISBN-10 0521820812
Release 2003-10-23
Pages 879
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Based on lectures given in honour of Stephen Hawking's sixtieth birthday, this book comprises contributions from some of the world's leading theoretical physicists. It begins with a section containing chapters by successful scientific popularisers, bringing to life both Hawking's work and other exciting developments in physics. The book then goes on to provide a critical evaluation of advanced subjects in modern cosmology and theoretical physics. Topics covered include the origin of the universe, warped spacetime, cosmological singularities, quantum gravity, black holes, string theory, quantum cosmology and inflation. As well as providing a fascinating overview of the wide variety of subject areas to which Stephen Hawking has contributed, this book represents an important assessment of prospects for the future of fundamental physics and cosmology.

Stars and Relativity

Stars and Relativity Author Ya. B. Zel’dovich
ISBN-10 9780486171326
Release 2014-06-10
Pages 544
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Two of the greatest astrophysicists of the 20th century explore general relativity, properties of matter under astrophysical conditions, stars, and stellar systems. A valuable resource for physicists, astronomers, graduate students. 1971 edition.

Introduction to General Relativity Black Holes and Cosmology

Introduction to General Relativity  Black Holes  and Cosmology Author Yvonne Choquet-Bruhat
ISBN-10 9780199666461
Release 2015-01-21
Pages 279
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General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics. Based on Yvonne Choquet-Bruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the foundations and main consequences of General Relativity. The first five chapters from General Relativity and the Einstein Equations have been updated with new sections and chapters on black holes, gravitational waves, singularities, and the Reissner-Nordstrom and interior Schwarzchild solutions. The rigour behind this book will provide readers with the perfect preparation to follow the great mathematical progress in the actual development, as well as the ability to model, the latest astrophysical and cosmological observations. The book presents basic General Relativity and provides a basis for understanding and using the fundamental theory.

Black Holes Thermodynamics Information and Firewalls

Black Holes  Thermodynamics  Information  and Firewalls Author Robert B. Mann
ISBN-10 9783319144962
Release 2015-03-05
Pages 97
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This book reflects the resurgence of interest in the quantum properties of black holes, culminating most recently in controversial discussions about firewalls. On the thermodynamic side, it describes how new developments allowed the inclusion of pressure/volume terms in the first law, leading to a new understanding of black holes as chemical systems, experiencing novel phenomena such as triple points and reentrant phase transitions. On the quantum-information side, the reader learns how basic arguments undergirding quantum complementarity have been shown to be flawed; and how this suggests that a black hole may surround itself with a firewall: a violent and chaotic region of highly excited states. In this thorough and pedagogical treatment, Robert Mann traces these new developments from their roots to our present-day understanding, highlighting their relationships and the challenges they present for quantum gravity.

The Geometry and Physics of Knots

The Geometry and Physics of Knots Author Michael Francis Atiyah
ISBN-10 0521395542
Release 1990-08-23
Pages 78
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Deals with an area of research that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.

Black Holes and Time Warps

Black Holes and Time Warps Author Kip S. Thorne
ISBN-10 0393312763
Release 1994
Pages 619
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Examines such phenomena as black holes, wormholes, singularities, gravitational waves, and time machines, exploring the fundamental principles that control the universe.

Einstein s Enigma or Black Holes in My Bubble Bath

Einstein s Enigma or Black Holes in My Bubble Bath Author C.V. Vishveshwara
ISBN-10 9783540332008
Release 2006-11-03
Pages 360
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This is a fascinating and enjoyable popular science book on gravity and black holes. It offers an absorbing account on the history of research on the universe and gravity from Aristotle via Copernicus via Newton to Einstein. The author possesses high literary qualities and is celebrated relativist. The physics of black holes constitutes one of the most fascinating chapters in modern science. At the same time, there is a fanciful quality associated with this strange and beautiful entity. The black hole story is undoubtedly an adventure through physics, philosophy, history, fiction and fantasy. This book is an attempt to blend all these elements together.


Gravity Author Eric Poisson
ISBN-10 9781139952392
Release 2014-05-29
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This textbook explores approximate solutions to general relativity and their consequences. It offers a unique presentation of Einstein's theory by developing powerful methods that can be applied to astrophysical systems. Beginning with a uniquely thorough treatment of Newtonian gravity, the book develops post-Newtonian and post-Minkowskian approximation methods to obtain weak-field solutions to the Einstein field equations. The book explores the motion of self-gravitating bodies, the physics of gravitational waves, and the impact of radiative losses on gravitating systems. It concludes with a brief overview of alternative theories of gravity. Ideal for graduate courses on general relativity and relativistic astrophysics, the book examines real-life applications, such as planetary motion around the Sun, the timing of binary pulsars, and gravitational waves emitted by binary black holes. Text boxes explore related topics and provide historical context, and over 100 exercises present challenging tests of the material covered in the main text.

Complex Analysis and Dynamical Systems VI Part 1 PDE Differential Geometry Radon Transform

Complex Analysis and Dynamical Systems VI  Part 1  PDE  Differential Geometry  Radon Transform Author Matania Ben-Artzi
ISBN-10 9781470416539
Release 2015-12-03
Pages 313
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This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19-24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers in this volume range over a wide variety of topics in Partial Differential Equations, Differential Geometry, and the Radon Transform. Taken together, the articles collected here provide the reader with a panorama of activity in partial differential equations and general relativity, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 667) is devoted to complex analysis, quasiconformal mappings, and complex dynamics. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).

A Modern Course in Statistical Physics

A Modern Course in Statistical Physics Author Linda E. Reichl
ISBN-10 9783527690466
Release 2016-11-22
Pages 482
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A Modern Course in Statistical Physics is a textbook that illustrates the foundations of equilibrium and non-equilibrium statistical physics, and the universal nature of thermodynamic processes, from the point of view of contemporary research problems. The book treats such diverse topics as the microscopic theory of critical phenomena, superfluid dynamics, quantum conductance, light scattering, transport processes, and dissipative structures, all in the framework of the foundations of statistical physics and thermodynamics. It shows the quantum origins of problems in classical statistical physics. One focus of the book is fluctuations that occur due to the discrete nature of matter, a topic of growing importance for nanometer scale physics and biophysics. Another focus concerns classical and quantum phase transitions, in both monatomic and mixed particle systems. This fourth edition extends the range of topics considered to include, for example, entropic forces, electrochemical processes in biological systems and batteries, adsorption processes in biological systems, diamagnetism, the theory of Bose-Einstein condensation, memory effects in Brownian motion, the hydrodynamics of binary mixtures. A set of exercises and problems is to be found at the end of each chapter and, in addition, solutions to a subset of the problems is provided. The appendices cover Exact Differentials, Ergodicity, Number Representation, Scattering Theory, and also a short course on Probability.