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| spacetime and geometry an introduction to general relativity: Spacetime and Geometry: An Introduction to General Relativity Sean Carroll, 2014-03-20 Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general relativity for advanced undergraduates and graduate students. It introduces modern techniques and an accessible and lively writing style to what can often be a formal and intimidating subject. Readers are led from physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology. Subtle points are illuminated throughout the text by careful and entertaining exposition. A straightforward and lucid approach, balancing mathematical rigor and physical insight, are hallmarks of this important text. The full text downloaded to your computer With eBooks you can: search for key concepts, words and phrases make highlights and notes as you study share your notes with friends eBooks are downloaded to your computer and accessible either offline through the Bookshelf (available as a free download), available online and also via the iPad and Android apps. Upon purchase, you'll gain instant access to this eBook. Time limit The eBooks products do not have an expiry date. You will continue to access your digital ebook products whilst you have your Bookshelf installed. |
| spacetime and geometry an introduction to general relativity: Spacetime and Geometry Sean M. Carroll, 2019-08-08 An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications. |
| spacetime and geometry an introduction to general relativity: The Geometry of Spacetime James J. Callahan, 2013-03-09 In 1905, Albert Einstein offered a revolutionary theory - special relativity - to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborates to gain objective knowledge of the world. He has tried to encompass both the general and special theory by using the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus. |
| spacetime and geometry an introduction to general relativity: Introduction To General Relativity And Cosmology Christian G Boehmer, 2016-10-06 Introduction to General Relativity and Cosmology gives undergraduate students an overview of the fundamental ideas behind the geometric theory of gravitation and spacetime. Through pointers on how to modify and generalise Einstein's theory to enhance understanding, it provides a link between standard textbook content and current research in the field.Chapters present complicated material practically and concisely, initially dealing with the mathematical foundations of the theory of relativity, in particular differential geometry. This is followed by a discussion of the Einstein field equations and their various properties. Also given is analysis of the important Schwarzschild solutions, followed by application of general relativity to cosmology. Questions with fully worked answers are provided at the end of each chapter to aid comprehension and guide learning. This pared down textbook is specifically designed for new students looking for a workable, simple presentation of some of the key theories in modern physics and mathematics. |
| spacetime and geometry an introduction to general relativity: Gravity James B. Hartle, 2021-06-24 Einstein's theory of general relativity is a cornerstone of modern physics. It also touches upon a wealth of topics that students find fascinating – black holes, warped spacetime, gravitational waves, and cosmology. Now reissued by Cambridge University Press, this ground-breaking text helped to bring general relativity into the undergraduate curriculum, making it accessible to virtually all physics majors. One of the pioneers of the 'physics-first' approach to the subject, renowned relativist James B. Hartle, recognized that there is typically not enough time in a short introductory course for the traditional, mathematics-first, approach. In this text, he provides a fluent and accessible physics-first introduction to general relativity that begins with the essential physical applications and uses a minimum of new mathematics. This market-leading text is ideal for a one-semester course for undergraduates, with only introductory mechanics as a prerequisite. |
| spacetime and geometry an introduction to general relativity: Spacetime Marcus Kriele, 2003-07-01 One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations and causality weak shell very crossing These singularities. add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach. |
| spacetime and geometry an introduction to general relativity: General Relativity Robert M. Wald, 1984-06-15 Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding.—S. Chandrasekhar A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect.—L. P. Hughston, Times Higher Education Supplement Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come.—James W. York, Physics Today |
| spacetime and geometry an introduction to general relativity: A First Course in General Relativity Bernard Schutz, 2009-05-14 Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background. |
| spacetime and geometry an introduction to general relativity: General Relativity Without Calculus Jose Natario, 2011-07-30 “General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding. |
| spacetime and geometry an introduction to general relativity: A General Relativity Workbook Thomas A. Moore, 2012-12-10 A General Relativity Workbook is a textbook intended to support a one-semester undergraduate course on general relativity. Through its unique workbook-based design, it enables students to develop a solid mastery of both the physics and the supporting tensor calculus by guiding them to work through the implications. The mathematics is introduced gradually and in a completely physical context. Each chapter, which is designed to correspond to one class session, involves a short overview of the concepts without obscuring derivations or details, followed by a series of boxes that guide students through the process of working things out. This active-learning approach enables students to develop a more secure mastery of the material than more traditional approaches. More than 350 homework problems support further learning. |
| spacetime and geometry an introduction to general relativity: Mathematical Introduction To General Relativity, A (Second Edition) Amol Sasane, 2024-12-20 The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe. Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to all the 283 exercises are included.The second edition corrects errors from the first edition, and includes 60 new exercises, 10 new remarks, 29 new figures, some of which cover auxiliary topics that were omitted in the first edition. |
| spacetime and geometry an introduction to general relativity: An Introduction to General Relativity L. P. Hughston, K. P. Tod, 1990 This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text. |
| spacetime and geometry an introduction to general relativity: Introduction to General Relativity, Black Holes, and Cosmology Yvonne Choquet-Bruhat, 2015 A precise yet simple introduction to the foundations and main consequences of General Relativity. The first five chapters from Choquet-Bruhat's General Relativity and the Einstein Equations (2008) have been updated with new sections and chapters on black holes, gravitational waves, singularities and more to form this textbook. |
| spacetime and geometry an introduction to general relativity: Problem Book in Relativity and Gravitation Alan P Lightman, William H. Press, Richard H. Price, Saul A. Teukolsky, 2017-09-01 An essential resource for learning about general relativity and much more, from four leading experts Important and useful to every student of relativity, this book is a unique collection of some 475 problems--with solutions--in the fields of special and general relativity, gravitation, relativistic astrophysics, and cosmology. The problems are expressed in broad physical terms to enhance their pertinence to readers with diverse backgrounds. In their solutions, the authors have attempted to convey a mode of approach to these kinds of problems, revealing procedures that can reduce the labor of calculations while avoiding the pitfall of too much or too powerful formalism. Although well suited for individual use, the volume may also be used with one of the modem textbooks in general relativity. |
| spacetime and geometry an introduction to general relativity: Einstein's Space-Time Rafael Ferraro, 2007-09-23 This excellent textbook offers a unique take on relativity theory, setting it in its historical context. Ideal for those interested in relativity and the history of physics, the book contains a complete account of special relativity that begins with the historical analysis of the reasons that led to a change in our view of space and time. Its aim is to foster a deep understanding of relativistic spacetime and its consequences for Dynamics. |
| spacetime and geometry an introduction to general relativity: Spacetime, Geometry and Gravitation Pankaj Sharan, 2009-11-18 This is an introductory book on the general theory of relativity based partly on lectures given to students of M.Sc. Physics at my university. The book is divided into three parts. The ?rst part is a preliminary course on general relativity with minimum preparation. The second part builds the ma- ematical background and the third part deals with topics where mathematics developed in the second part is needed. The ?rst chapter gives a general background and introduction. This is f- lowed by an introduction to curvature through Gauss’ Theorema Egregium. This theorem expresses the curvature of a two-dimensional surface in terms of intrinsic quantitiesrelatedtothein?nitesimaldistancefunctiononthesurface.Thestudent isintroducedtothemetrictensor,Christo?elsymbolsandRiemanncurvaturet- sor by elementary methods in the familiar and visualizable case of two dimensions. This early introduction to geometric quantities equips a student to learn simpler topics in general relativity like the Newtonian limit, red shift, the Schwarzschild solution, precession of the perihelion and bending of light in a gravitational ?eld. Part II (chapters 5 to 10) is an introduction to Riemannian geometry as - quired by general relativity. This is done from the beginning, starting with vectors and tensors. I believe that students of physics grasp physical concepts better if they are not shaky about the mathematics involved. |
| spacetime and geometry an introduction to general relativity: Spacetime Physics Edwin F. Taylor, John Archibald Wheeler, 1992-03-15 This thoroughly up-to-date, highly accessible overview covers microgravity, collider accelerators, satellite probes, neutron detectors, radioastronomy, and pulsars. |
| spacetime and geometry an introduction to general relativity: Relativity, Gravitation and Cosmology Ta-Pei Cheng, 2010 An introduction to Einstein's general theory of relativity, this work is structured so that interesting applications, such as gravitational lensing, black holes and cosmology, can be presented without the readers having to first learn the difficult mathematics of tensor calculus. |
| spacetime and geometry an introduction to general relativity: General Relativity Steven Carlip, 2019 This is a short textbook on general relativity and gravitation aimed at readers with a broad range of interests in physics, from cosmology to high energy physics to condensed matter. The approach is physics first: readers move quickly to the calculation of observational predictions and only then return to mathematical foundations.-- |
| spacetime and geometry an introduction to general relativity: Spacetime and Geometry Sean Carroll, 2013-08 Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general relativity for advanced undergraduates and graduate students. It introduces modern techniques and an accessible and lively writing style to what can often be a formal and intimidating subject. Readers are led from physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology. Subtle points are illuminated throughout the text by careful and entertaining exposition. A straightforward and lucid approach, balancing mathematical rigor and physical insight, are hallmarks of this important text. |
| spacetime and geometry an introduction to general relativity: A Short Course in General Relativity James A. Foster, J. David Nightingale, 2010-04-30 Suitable for a one-semester course in general relativity for senior undergraduates or beginning graduate students, this text clarifies the mathematical aspects of Einstein's theory of relativity without sacrificing physical understanding. The text begins with an exposition of those aspects of tensor calculus and differential geometry needed for a proper treatment of the subject. The discussion then turns to the spacetime of general relativity and to geodesic motion. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes and rotating objects. The main text concludes with introductory chapters on gravitational radiation and cosmology. This new third edition has been updated to take account of fresh observational evidence and experiments. It includes new sections on the Kerr solution (in Chapter 4) and cosmological speeds of recession (in Chapter 6). A more mathematical treatment of tensors and manifolds, included in the 1st edition, but omitted in the 2nd edition, has been restored in an appendix. Also included are two additional appendixes – Special Relativity Review and The Chinese Connection - and outline solutions to all exercises and problems, making it especially suitable for private study. |
| spacetime and geometry an introduction to general relativity: Differential Geometry and Relativity Theory RichardL. Faber, 2017-10-19 Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force. Uniting differential geometry and both special and generalrelativity in a single source, this easy-to-understand text opens the general theory of relativityto mathematics majors having a backgr.ound only in multivariable calculus and linearalgebra.The book offers a broad overview of the physical foundations and mathematical details ofrelativity, and presents concrete physical interpretations of numerous abstract concepts inRiemannian geometry. The work is profusely illustrated with diagrams aiding in the understandingof proofs and explanations. Appendices feature important material on vectoranalysis and hyperbolic functions.Differential Geometry and Relativity Theory: An Introduction serves as the ideal textfor high-level undergraduate couues in mathematics and physics, and includes a solutionsmanual augmenting classroom study. It is an invaluable reference for mathematicians interestedin differential and IUemannian geometry, or the special and general theories ofrelativity |
| spacetime and geometry an introduction to general relativity: The Geometry of Minkowski Spacetime Gregory L. Naber, 2003-01-01 This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; an in-depth introduction to the theory of spinors; and a classification of electromagnetic fields in both tensor and spinor form. Appendixes introduce a topology for Minkowski spacetime and discuss Dirac's famous Scissors Problem. Appropriate for graduate-level courses, this text presumes only a knowledge of linear algebra and elementary point-set topology. 1992 edition. 43 figures. |
| spacetime and geometry an introduction to general relativity: General Relativity Michael Paul Hobson, George Efstathiou, Anthony N. Lasenby, 2006 Written for advanced undergraduate and graduate students, this is a clear mathematical introduction to Einstein's theory of general relativity and its physical applications. Concentrating on the theory's physical consequences, this approachable textbook contains over 300 exercises to illuminate and extend the discussion. |
| spacetime and geometry an introduction to general relativity: Modern General Relativity M. W. Guidry, Mike Guidry, 2019-01-03 Introduces the physics of general relativity in relation to modern topics such as gamma-ray bursts, black holes, and gravitational waves. |
| spacetime and geometry an introduction to general relativity: Relativity Steve Adams, 2017-06-30 Provides the essential principles and results of special relativity as required by undergraduates. The text uses a geometric interpretation of space-time so that a general theory is seen as a natural extension of the special theory. Although most results are derived from first principles, complex and distracting mathematics is avoided and all mathe |
| spacetime and geometry an introduction to general relativity: Einstein Gravity in a Nutshell A. Zee, 2013-05-05 An ideal introduction to Einstein's general theory of relativity This unique textbook provides an accessible introduction to Einstein's general theory of relativity, a subject of breathtaking beauty and supreme importance in physics. With his trademark blend of wit and incisiveness, A. Zee guides readers from the fundamentals of Newtonian mechanics to the most exciting frontiers of research today, including de Sitter and anti-de Sitter spacetimes, Kaluza-Klein theory, and brane worlds. Unlike other books on Einstein gravity, this book emphasizes the action principle and group theory as guides in constructing physical theories. Zee treats various topics in a spiral style that is easy on beginners, and includes anecdotes from the history of physics that will appeal to students and experts alike. He takes a friendly approach to the required mathematics, yet does not shy away from more advanced mathematical topics such as differential forms. The extensive discussion of black holes includes rotating and extremal black holes and Hawking radiation. The ideal textbook for undergraduate and graduate students, Einstein Gravity in a Nutshell also provides an essential resource for professional physicists and is accessible to anyone familiar with classical mechanics and electromagnetism. It features numerous exercises as well as detailed appendices covering a multitude of topics not readily found elsewhere. Provides an accessible introduction to Einstein's general theory of relativity Guides readers from Newtonian mechanics to the frontiers of modern research Emphasizes symmetry and the Einstein-Hilbert action Covers topics not found in standard textbooks on Einstein gravity Includes interesting historical asides Features numerous exercises and detailed appendices Ideal for students, physicists, and scientifically minded lay readers Solutions manual (available only to teachers) |
| spacetime and geometry an introduction to general relativity: Gravitation Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, 2017-10-24 Spacetime physics -- Physics in flat spacetime -- The mathematics of curved spacetime -- Einstein's geometric theory of gravity -- Relativistic stars -- The universe -- Gravitational collapse and black holes -- Gravitational waves -- Experimental tests of general relativity -- Frontiers |
| spacetime and geometry an introduction to general relativity: Elements of General Relativity Piotr T. Chruściel, 2020-03-19 This book provides an introduction to the mathematics and physics of general relativity, its basic physical concepts, its observational implications, and the new insights obtained into the nature of space-time and the structure of the universe. It introduces some of the most striking aspects of Einstein's theory of gravitation: black holes, gravitational waves, stellar models, and cosmology. It contains a self-contained introduction to tensor calculus and Riemannian geometry, using in parallel the language of modern differential geometry and the coordinate notation, more familiar to physicists. The author has strived to achieve mathematical rigour, with all notions given careful mathematical meaning, while trying to maintain the formalism to the minimum fit-for-purpose. Familiarity with special relativity is assumed. The overall aim is to convey some of the main physical and geometrical properties of Einstein's theory of gravitation, providing a solid entry point to further studies of the mathematics and physics of Einstein equations. |
| spacetime and geometry an introduction to general relativity: Spacetime and Geometry Sean M. Carroll, 2019-08-08 Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first covers the foundations of the theory and mathematical formalism, providing an approachable introduction to what can often be an intimidating subject. Three major applications of general relativity are then discussed: black holes, perturbation theory and gravitational waves, and cosmology. Students will learn the origin of how spacetime curves (the Einstein equation) and how matter moves through it (the geodesic equation). They will learn what black holes really are, how gravitational waves are generated and detected, and the modern view of the expansion of the universe. A brief introduction to quantum field theory in curved spacetime is also included. A student familiar with this book will be ready to tackle research-level problems in gravitational physics. |
| spacetime and geometry an introduction to general relativity: General Relativity Hans Stephani, 1990-06-29 This book is an excellent introduction to the subjects of gravitation and space-time structure. It presumes a good background in special relativity, electrodynamics, and classical mechanics. The book discusses the foundations of Riemannian geometry; the derivation of the Einstein field equations; linearised theory, far fields and gravitational waves; the invariant characterization of exact solutions; gravitational collapse; cosmology; and a final chapter deals with alternative gravitation theories and the problem of quantum gravity. This revised and correct edition brings the experimental evidence up to date. In addition, the sections on quantum gravity have been rewritten and enlarged, and now form a coherent introduction to this subject. |
| spacetime and geometry an introduction to general relativity: Modern Differential Geometry for Physicists Chris J. Isham, 1999 The result is a book which provides a rapid initiation to the material in question with care and sufficient detail to allow the reader to emerge with a genuine familiarity with the foundations of these subjects.Mathematical ReviewsThis book is carefully written, and attention is paid to rigor and relevant details The key notions are discussed with great care and from many points of view, which attenuates the shock of the formalism. Mathematical Reviews |
| spacetime and geometry an introduction to general relativity: Special Relativity, Electrodynamics, and General Relativity John B. Kogut, 2018-01-09 Special Relativity, Electrodynamics, and General Relativity: From Newton to Einstein is intended to teach students of physics, astrophysics, astronomy, and cosmology how to think about special and general relativity in a fundamental but accessible way. Designed to render any reader a master of relativity, all material on the subject is comprehensible and derivable from first principles. The book emphasizes problem solving, contains abundant problem sets, and is conveniently organized to meet the needs of both student and instructor. - Fully revised and expanded second edition with improved figures - Enlarged discussion of dynamics and the relativistic version of Newton's second law - Resolves the twin paradox from the principles of special and general relativity - Includes new chapters which derive magnetism from relativity and electrostatics - Derives Maxwell's equations from Gauss' law and the principles of special relativity - Includes new chapters on differential geometry, space-time curvature, and the field equations of general relativity - Introduces black holes and gravitational waves as illustrations of the principles of general relativity and relates them to the 2015 and 2017 observational discoveries of LIGO |
| spacetime and geometry an introduction to general relativity: Introduction to General Relativity Lewis Ryder, 2020-01-16 A student-friendly style, over 100 illustrations, and numerous exercises are brought together in this textbook for advanced undergraduate and beginning graduate students in physics and mathematics. Lewis Ryder develops the theory of general relativity in detail. Covering the core topics of black holes, gravitational radiation, and cosmology, he provides an overview of general relativity and its modern ramifications. The book contains chapters on gravitational radiation, cosmology, and connections between general relativity and the fundamental physics of the microworld. It explains the geometry of curved spaces and contains key solutions of Einstein's equations - the Schwarzschild and Kerr solutions. Mathematical calculations are worked out in detail, so students can develop an intuitive understanding of the subject, as well as learn how to perform calculations. The book also includes topics concerned with the relation between general relativity and other areas of fundamental physics. Selected solutions for instructors are available under Resources. |
| spacetime and geometry an introduction to general relativity: Exact Space-Times in Einstein's General Relativity Jerry B. Griffiths, Jiří Podolský, 2009-10-15 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. |
| spacetime and geometry an introduction to general relativity: 3+1 Formalism in General Relativity Éric Gourgoulhon, 2012-02-27 This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book. |
| spacetime and geometry an introduction to general relativity: Relativity Made Relatively Easy Andrew M. Steane, 2012-10-04 This book unfolds the subject of Relativity for undergraduate students of physics. It fills a gap between introductory descriptions and texts for researchers. Assuming almost no prior knowledge, it allows the student to handle all the Relativity needed for a university course, with explanations as simple, thorough, and engaging as possible. |
| spacetime and geometry an introduction to general relativity: A First Course in General Relativity Bernard F. Schutz, 1985-01-31 This textbook develops general relativity and its associated mathematics from a minimum of prerequisites, leading to a physical understanding of the theory in some depth. |
| spacetime and geometry an introduction to general relativity: Introduction to 2-spinors in General Relativity Peter J. O'Donnell, 2003 This book deals with 2-spinors in general relativity, beginning by developing spinors in a geometrical way rather than using representation theory, which can be a little abstract. This gives the reader greater physical intuition into the way in which spinors behave. The book concentrates on the algebra and calculus of spinors connected with curved space-time. Many of the well-known tensor fields in general relativity are shown to have spinor counterparts. An analysis of the Lanczos spinor concludes the book, and some of the techniques so far encountered are applied to this. Exercises play an important role throughout and are given at the end of each chapter. |
| spacetime and geometry an introduction to general relativity: The Large Scale Structure of Space-Time S. W. Hawking, G. F. R. Ellis, 1975-02-27 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. |
Spacetime and Geometry: An Introduction to General Rel…
Jan 1, 2003 · Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general …
Spacetime and Geometry An Introduction to General Rel…
Aug 15, 2019 · Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first …
Spacetime and Geometry : An Introduction to General Rel…
Readers are led from physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to …
SpacetimeandGeometry - Cambridge University Pres…
Spacetime and Geometry is an introductory textbook on general relativity, speci cally aimed at students. Using a lucid style, Carroll rst covers …
[PDF] Spacetime and Geometry by Sean M. Carroll …
Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first …
Spacetime and Geometry: An Introduction to General Rel…
Jan 1, 2003 · Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general …
Spacetime and Geometry An Introduction to General Rel…
Aug 15, 2019 · Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first …
Spacetime and Geometry : An Introduction to General Rel…
Readers are led from physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to …
SpacetimeandGeometry - Cambridge University Pres…
Spacetime and Geometry is an introductory textbook on general relativity, speci cally aimed at students. Using a lucid style, Carroll rst covers …
[PDF] Spacetime and Geometry by Sean M. Carroll …
Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first …
