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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.

General Relativity

General Relativity Author Norbert Straumann
ISBN-10 9783662118276
Release 2013-11-11
Pages 676
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The foundations are thoroughly developed together with the required mathematical background from differential geometry developed in Part III. The author also discusses the tests of general relativity in detail, including binary pulsars, with much space is devoted to the study of compact objects, especially to neutron stars and to the basic laws of black-hole physics. This well-structured text and reference enables readers to easily navigate through the various sections as best matches their backgrounds and perspectives, whether mathematical, physical or astronomical. Very applications oriented, the text includes very recent results, such as the supermassive black-hole in our galaxy and first double pulsar system

Physical Foundations of Cosmology

Physical Foundations of Cosmology Author Viatcheslav Mukhanov
ISBN-10 9781139447119
Release 2005-11-10
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Inflationary cosmology has been developed over the last twenty years to remedy serious shortcomings in the standard hot big bang model of the universe. This textbook, first published in 2005, explains the basis of modern cosmology and shows where the theoretical results come from. The book is divided into two parts; the first deals with the homogeneous and isotropic model of the Universe, the second part discusses how inhomogeneities can explain its structure. Established material such as the inflation and quantum cosmological perturbation are presented in great detail, however the reader is brought to the frontiers of current cosmological research by the discussion of more speculative ideas. An ideal textbook for both advanced students of physics and astrophysics, all of the necessary background material is included in every chapter and no prior knowledge of general relativity and quantum field theory is assumed.

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.

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.

Collected Papers on Ricci Flow

Collected Papers on Ricci Flow Author Huai-Dong Cao
ISBN-10 1571461108
Release 2003
Pages 539
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The Ricci flow is a hot topic at the forefront of mathematics research. This selection of papers on the Riemannian Ricci flow is intended both for the graduate student or researcher unfamiliar with the Ricci flow and for geometers already familiar to the Ricci flow.

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.

Topics in the Foundations of General Relativity and Newtonian Gravitation Theory

Topics in the Foundations of General Relativity and Newtonian Gravitation Theory Author David B. Malament
ISBN-10 9780226502472
Release 2012-04-02
Pages 368
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In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Gödel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is no criterion of orbital rotation in general relativity that fully answers to our classical intuitions. Topics is intended for both students and researchers in mathematical physics and philosophy of science.

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 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.

Advanced General Relativity

Advanced General Relativity Author John Stewart
ISBN-10 0521449464
Release 1993-11-26
Pages 228
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A self-contained introduction to advanced general relativity.

Hawking Radiation From Astrophysical Black Holes To Analogous Systems In Lab

Hawking Radiation  From Astrophysical Black Holes To Analogous Systems In Lab Author Belgiorno Francesco D
ISBN-10 9789814508551
Release 2000-03-21
Pages 340
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Hawking Radiation From Astrophysical Black Holes To Analogous Systems In Lab has been writing in one form or another for most of life. You can find so many inspiration from Hawking Radiation From Astrophysical Black Holes To Analogous Systems In Lab also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Hawking Radiation From Astrophysical Black Holes To Analogous Systems In Lab book for free.

General Relativity

General Relativity Author N.M.J. Woodhouse
ISBN-10 1846284872
Release 2007-03-06
Pages 220
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Based on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.