Lecture Notes on the General Theory of Relativity

Author: Øyvind Grøn
Publisher: Springer Science & Business Media
ISBN: 9780387881348
Release Date: 2010-03-23
Genre: Science

This book collects lectures on the general theory of relativity given by Dr. Øyvind Grøn at the University of Oslo, Norway. This accessible text allows students to follow the deductions all the way throughout the book.

General Relativity Without Calculus

Author: Jose Natario
Publisher: Springer Science & Business Media
ISBN: 3642214525
Release Date: 2011-08-01
Genre: Science

“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.

Einstein s General Theory of Relativity

Author: Øyvind Grøn
Publisher: Springer Science & Business Media
ISBN: 9780387692005
Release Date: 2007-08-24
Genre: Science

This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.

General Relativity

Author: Robert Geroch
Publisher: Minkowski Institute Press
ISBN: 9780987987181
Release Date: 2013-02-25

Robert Geroch's lecture notes on general relativity are unique in three main respects. First, the physics of general relativity and the mathematics, which describes it, are masterfully intertwined in such a way that both reinforce each other to facilitate the understanding of the most abstract and subtle issues. Second, the physical phenomena are first properly explained in terms of spacetime and then it is shown how they can be “decomposed” into familiar quantities, expressed in terms of space and time, which are measured by an observer. Third, Geroch's successful pedagogical approach to teaching theoretical physics through visualization of even the most abstract concepts is fully applied in his lectures on general relativity by the use of around a hundred figures. Although the book contains lecture notes written in 1972, it is (and will remain) an excellent introduction to general relativity, which covers its physical foundations, its mathematical formalism, the classical tests of its predictions, its application to cosmology, a number of specific and important issues (such as the initial value formulation of general relativity, signal propagation, time orientation, causality violation, singularity theorems, conformal transformations, and asymptotic structure of spacetime), and the early approaches to quantization of the gravitational field. Geroch's Differential Geometry: 1972 Lecture Notes can serve as a very helpful companion to this book.


Author: Marcus Kriele
Publisher: Springer Science & Business Media
ISBN: 9783540483540
Release Date: 2003-07-01
Genre: Science

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.

General Theory of Relativity

Author: P. A.M. Dirac
Publisher: Princeton University Press
ISBN: 9781400884193
Release Date: 2016-08-10
Genre: Science

Einstein's general theory of relativity requires a curved space for the description of the physical world. If one wishes to go beyond superficial discussions of the physical relations involved, one needs to set up precise equations for handling curved space. The well-established mathematical technique that accomplishes this is clearly described in this classic book by Nobel Laureate P.A.M. Dirac. Based on a series of lectures given by Dirac at Florida State University, and intended for the advanced undergraduate, General Theory of Relativity comprises thirty-five compact chapters that take the reader point-by-point through the necessary steps for understanding general relativity.

Lectures on General Relativity

Author: A. Papapetrou
Publisher: Springer Science & Business Media
ISBN: 9789401022774
Release Date: 2012-12-06
Genre: Science

This book is an elaboration of lecture notes for the graduate course on General Rela tivity given by the author at Boston University in the spring semester of 1972. It is an introduction to the subject only, as the time available for the course was limited. The author of an introduction to General Relativity is faced from the beginning with the difficult task of choosing which material to include. A general criterion as sisting in this choice is provided by the didactic character of the book: Those chapters have to be included in priority, which will be most useful to the reader in enabling him to understand the methods used in General Relativity, the results obtained so far and possibly the problems still to be solved. This criterion is not sufficient to ensure a unique choice. General Relativity has developed to such a degree, that it is impossible to include in an introductory textbook of a reasonable length even a very condensed treatment of all important problems which have been discussed until now and the author is obliged to decide, in a more or less subjective manner, which of the more recent developments to omit. The following lines indicate by means of some examples the kind of choice made in this book.

The General Theory of Relativity

Author: Anadijiban Das
Publisher: Springer Science & Business Media
ISBN: 9781461436584
Release Date: 2012-06-26
Genre: Science

The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: tensor analysis the special theory of relativity the general theory of relativity and Einstein’s field equations spherically symmetric solutions and experimental confirmations static and stationary space-time domains black holes cosmological models algebraic classifications and the Newman-Penrose equations the coupled Einstein-Maxwell-Klein-Gordon equations appendices covering mathematical supplements and special topics Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland, Jadavpur University, India, Carnegie-Mellon University, USA, and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory. Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity.

Spacetime and Geometry

Author: Sean Carroll
ISBN: 1292026634
Release Date: 2013-08
Genre: Science

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.

Asymptotic Analysis in General Relativity

Author: Thierry Daudé
Publisher: Cambridge University Press
ISBN: 9781316649404
Release Date: 2018-01-11
Genre: Mathematics

Introduction to modern methods for classical and quantum fields in general relativity / Thierry Daudé, Dietrich Häfner, and Jean-Philippe Nicolas -- Geometry of black hole spacetimes / Lars Andersson, Thomas B. Ackdahl, and Pieter Blue -- An introduction to Quantum Field Theory on curved space-times / Christian Gerard -- A minicourse on microlocal analysis for wave propagation / Andras Vasy -- An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity / Sean N. Curry and A. Rod Gover

The Special Theory of Relativity

Author: Costas Christodoulides
Publisher: Springer
ISBN: 9783319252742
Release Date: 2016-02-09
Genre: Science

This book offers a comprehensive, university-level introduction to Einstein’s Special Theory of Relativity. In addition to the purely theoretical aspect, emphasis is also given to its historical development as well as to the experiments that preceded the theory and those performed in order to test its validity.The main body of the book consists of chapters on Relativistic Kinematics and Dynamics and their applications, Optics and Electromagnetism. These could be covered in a one-semester course. A more advanced course might include the subjects examined in the other chapters of the book and its appendices.As a textbook, it has some unique characteristics: It provides detailed proofs of the theorems, offers abundant figures and discusses numerous examples. It also includes a number of problems for readers to solve, the complete solutions of which are given at the end of the book.It is primarily intended for use by university students of physics, mathematics and engineering. However, as the mathematics needed is of an upper-intermediate level, the book will also appeal to a more general readership.

A First Course in General Relativity

Author: Bernard Schutz
Publisher: Cambridge University Press
ISBN: 9780521887052
Release Date: 2009-05-14
Genre: Science

Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.

Some Elementary Gauge Theory Concepts

Author: Hong-Mo Chan
Publisher: World Scientific
ISBN: 9789814505277
Release Date: 1993-09-22
Genre: Science

Gauge theory, which underlies modern particle physics as well as the theory of gravity, and hence all of physics as we know it today, is itself based on a few fundamental concepts, the consequences of which are often as beautiful as they are deep. Unfortunately, in view of the pressure to cover aspects of the theory that are necessary for its many important applications, very little space is usually devoted in textbooks and graduate courses to the treatment of these concepts. The present small volume is an attempt to help in some degree to redress this imbalance in the literature. The topics covered are elementary in the sense of being basic, not in the sense of being shallow or easy. Although all will already feature at the classical field level, and most even before the introduction of an action principle, they often lead one to pose some quite profound questions, so that much of the material treated is by necessity at the front line of research. The approach adopted is physically motivated, although there is no hesitation in introducing mathematical concepts when they are a help to understanding. In the presentation, little is assumed of the reader, and no pains has been spared to make the whole volume understandable to researchers in other fields and to graduate students, provided that the reader is willing to devote sufficient effort required by the subject matter. On the other hand, neither has there been any conscious attempt to avoid essential difficulties, or to trivialise concepts which are intrinsically abstruse. It is thus hoped that the result will be enjoyable reading for researchers and students alike. Contents:Basic ConceptsMonopolesMathematical InterludeLoop Space Formulation DynamicsGeneralized Gauge Structures Readership: Students and researchers in high energy physics and mathematical physicists. keywords:Gauge Theory Concepts;Yang-Mills Theory;Nonabelian Gauge Theory;Monopoles;Topological Charges;Loop Space;Electric-magnetic Duality;Nonabelian Duality;Half-strings;Noncommutative Gauge Theory “It is an elegant little book, which despite its brevity, vividly provides all the groundwork and basic ideas of gauge theory — so fundamental to modern theoretical physics.” Roger Penrose University of Oxford

Einstein Relatively Simple

Author: Ira Mark Egdall
Publisher: World Scientific
ISBN: 9789814525619
Release Date: 2014-01-06
Genre: Science

"Outstanding Academic Title for 2014" by CHOICE Einstein Relatively Simple brings together for the first time an exceptionally clear explanation of both special and general relativity. It is for people who always wanted to understand Einstein's ideas but never thought they could. Told with humor, enthusiasm, and rare clarity, this entertaining book reveals how a former high school drop-out revolutionized our understanding of space and time. From E=mc2 and everyday time travel to black holes and the big bang, Einstein Relatively Simple takes us all, regardless of our scientific backgrounds, on a mind-boggling journey through the depths of Einstein's universe. Along the way, we track Einstein through the perils and triumphs of his life — follow his thinking, his logic, and his insights — and chronicle the audacity, imagination, and sheer genius of the man recognized as the greatest scientist of the modern era. In Part I on special relativity we learn how time slows and space shrinks with motion, and how mass and energy are equivalent. Part II on general relativity reveals a cosmos where black holes trap light and stop time, where wormholes form gravitational time machines, where space itself is continually expanding, and where some 13.7 billion years ago our universe was born in the ultimate cosmic event — the Big Bang. Contents:Einstein Discovered: Special Relativity, E = mc2,and Spacetime:From Unknown to RevolutionaryThe Great ConflictThe Two PostulatesA New RealityThe Shrinking of TimeSimultaneity and the Squeezing of SpaceThe World's Most Famous EquationSpacetimeEinstein Revealed: General Relativity, Gravity, and the Cosmos:Einstein's Dream“The Happiest Thought of My Life”The Warping of Space and TimeStitching SpacetimeWhat is Spacetime Curvature?Einstein's MasterpieceThe Universe RevealedIn the Beginning Readership: Adults and young people all over the world who are curious about Einstein and how the universe works. Keywords:Einstein;Relativity;Special Relativity;General Relativity;Spacetime;Big Bang;Black Holes;Expansion of Space;Time Travel;E=mc2;Universe;Cosmos;Time Dilation;Length Contraction;Wormholes;Light Postulate;Length Contraction;Gravitational Time Dilation;Time Warp;Space Warp;Relativity Postulate;Lorentz Transformation;Light Clock;Relativity of Simultaneity;Twins Paradox;Equivalence Principle;Gravity;Spacetime Curvature;Spacetime Interval;Gaussian Co-Ordinates;Geodesic;Momenergy;The Einstein Equation;Schwarzschild Geometry;Bending of Starlight;Frame Dragging;Cosmic Microwave Background;Geometry of Universe;Flat Universe;Critical Density;Dark Matter;Dark Energy;Future of UniverseKey Features:Einstein Relatively Simple is the definitive book on Einstein's theories for the lay reader — one that is fun to read, comprehensive, and most important, understandableEinstein's ideas are explained in everyday languageThe book devotes eight chapters to special and a full eight chapters to general relativity. Most popular science books give general relativity only a brief mention or ignore it altogetherReviews: “This general relativity theory changed our views on the origin and on the ending (if any) of the universe … all topics that tickle the imagination of a general public and Egdall, bringing the reader to the point beyond general relativity, does not miss the opportunity to end his guided tour with a sparkling firework of these issues … it is an entertaining introduction for the layman, that brings the reader a very long way.” The European Mathematical Society “He covers the main topics of special and general relativity in a refreshing, personal way. This is a well-crafted, well-documented text with extensive endnotes, in which a bibliography is embedded. He introduces readers to his own unique entry into this very populous genre. Valuable for inquisitive nonscientists.” CHOICE “I'm crazy about it. It's the best presentation of relativity for non-scientists that I've seen.” Art Hobson Professor Emeritus of Physics University of Arkansas "The writing is jovial and energetic and holds the reader's attention. This book is a nice introduction to modern physics, with a great biography of Einstein included. This book is recommended for a lay reader with basic algebra skills; high school and beginning college physics students would find it easily accessible." Zentralblatt MATH