Spacetime and Geometry

An Introduction to General Relativity

Author: Sean Carroll

Publisher: N.A

ISBN: 9781292026633

Category: Science

Page: 513

View: 6838

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 Geometry of Spacetime

An Introduction to Special and General Relativity

Author: James J. Callahan

Publisher: Springer Science & Business Media

ISBN: 1475767366

Category: Science

Page: 463

View: 6211

Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.

General Relativity

An Introduction for Physicists

Author: M. P. Hobson,G. P. Efstathiou,A. N. Lasenby

Publisher: Cambridge University Press

ISBN: 9780521829519

Category: Science

Page: 572

View: 540

General Relativity: An Introduction for Physicists provides a clear mathematical introduction to Einstein's theory of general relativity. It presents a wide range of applications of the theory, concentrating on its physical consequences. After reviewing the basic concepts, the authors present a clear and intuitive discussion of the mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are then used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is then introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle. Written for advanced undergraduate and graduate students, this approachable textbook contains over 300 exercises to illuminate and extend the discussion in the text.

Spacetime and Geometry: Pearson New International Edition

An Introduction to General Relativity

Author: Sean Carroll

Publisher: Pearson Higher Ed

ISBN: 1292039019

Category: Science

Page: 528

View: 546

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

Foundations of General Relativity and Differential Geometry

Author: Marcus Kriele

Publisher: Springer Science & Business Media

ISBN: 3540483543

Category: Science

Page: 436

View: 3704

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, Geometry and Gravitation

Author: Pankaj Sharan

Publisher: Springer Science & Business Media

ISBN: 3764399716

Category: Science

Page: 355

View: 3483

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.

The Geometry of Minkowski Spacetime

An Introduction to the Mathematics of the Special Theory of Relativity

Author: Gregory L. Naber

Publisher: Springer Science & Business Media

ISBN: 1441978380

Category: Mathematics

Page: 324

View: 8364

This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title. Reviews of first edition: “... a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics.” (American Mathematical Society, 1993) “Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations.” (CHOICE, 1993) “... his talent in choosing the most significant results and ordering them within the book can’t be denied. The reading of the book is, really, a pleasure.” (Dutch Mathematical Society, 1993)

General Relativity

Author: Robert M. Wald

Publisher: University of Chicago Press

ISBN: 9780226870373

Category: Science

Page: 506

View: 8718

"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

An Introduction to General Relativity

Author: L. P. Hughston,K. P. Tod

Publisher: Cambridge University Press

ISBN: 9780521339438

Category: Mathematics

Page: 183

View: 6615

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.

Relativity, Gravitation and Cosmology

A Basic Introduction

Author: Ta-Pei Cheng

Publisher: Oxford University Press

ISBN: 0199573638

Category: Science

Page: 435

View: 528

This book provides an introduction to Einstein's general theory of relativity. A "physics-first" approach is adopted so that interesting applications come before the more difficult task of solving the Einstein equation. The book includes extensive coverage of cosmology, and is designed to allow readers to study the subject alone.

General Relativity

With Applications to Astrophysics

Author: Norbert Straumann

Publisher: Springer Science & Business Media

ISBN: 3662118270

Category: Science

Page: 676

View: 8998

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

The Geometry of Special Relativity

Author: Tevian Dray

Publisher: CRC Press

ISBN: 1466510471

Category: Mathematics

Page: 150

View: 7736

The Geometry of Special Relativity provides an introduction to special relativity that encourages readers to see beyond the formulas to the deeper geometric structure. The text treats the geometry of hyperbolas as the key to understanding special relativity. This approach replaces the ubiquitous γ symbol of most standard treatments with the appropriate hyperbolic trigonometric functions. In most cases, this not only simplifies the appearance of the formulas, but also emphasizes their geometric content in such a way as to make them almost obvious. Furthermore, many important relations, including the famous relativistic addition formula for velocities, follow directly from the appropriate trigonometric addition formulas. The book first describes the basic physics of special relativity to set the stage for the geometric treatment that follows. It then reviews properties of ordinary two-dimensional Euclidean space, expressed in terms of the usual circular trigonometric functions, before presenting a similar treatment of two-dimensional Minkowski space, expressed in terms of hyperbolic trigonometric functions. After covering special relativity again from the geometric point of view, the text discusses standard paradoxes, applications to relativistic mechanics, the relativistic unification of electricity and magnetism, and further steps leading to Einstein’s general theory of relativity. The book also briefly describes the further steps leading to Einstein’s general theory of relativity and then explores applications of hyperbola geometry to non-Euclidean geometry and calculus, including a geometric construction of the derivatives of trigonometric functions and the exponential function.

Gravitational Curvature

An Introduction to Einstein's Theory

Author: Theodore Frankel

Publisher: Courier Corporation

ISBN: 048628915X

Category: Science

Page: 192

View: 5075

This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence and stresses the global aspects of cosmology. Suitable for independent study as well as for courses in differential geometry, relativity, and cosmology. 1979 edition.

Gravity from the Ground Up

An Introductory Guide to Gravity and General Relativity

Author: Bernard Schutz

Publisher: Cambridge University Press

ISBN: 1139457349

Category: Science

Page: N.A

View: 9132

This book invites the reader to understand our Universe, not just marvel at it. From the clock-like motions of the planets to the catastrophic collapse of a star into a black hole, gravity controls the Universe. Gravity is central to modern physics, helping to answer the deepest questions about the nature of time, the origin of the Universe and the unification of the forces of nature. Linking key experiments and observations through careful physical reasoning, the author builds the reader's insight step-by-step from simple but profound facts about gravity on Earth to the frontiers of research. Topics covered include the nature of stars and galaxies, the mysteries of dark matter and dark energy, black holes, gravitational waves, inflation and the Big Bang. Suitable for general readers and for undergraduate courses, the treatment uses only high-school level mathematics, supplemented by optional computer programs, to explain the laws of physics governing gravity.

Space, Time, and Gravity

The Theory of the Big Bang and Black Holes

Author: Robert M. Wald

Publisher: University of Chicago Press

ISBN: 9780226870281

Category: Science

Page: 153

View: 8088

Writing for the general reader or student, Wald has completely revised and updated this highly regarded work to include recent developments in black hole physics and cosmology. Nature called the first edition "a very readable and accurate account of modern relativity physics for the layman within the unavoidable constraint of almost no mathematics. . . . A well written, entertaining and authoritative book."

Gravity

An Introduction to Einstein's General Relativity

Author: James B. Hartle

Publisher: Pearson

ISBN: 9781292039145

Category: Science

Page: 554

View: 9486

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. Until now, it has not been included in the curriculum of many undergraduate physics courses because the required math is too advanced. The aim of this ground-breaking new text is to bring general relativity into the undergraduate curriculum and make this fundamental theory accessible to virtually all physics majors. Using a physics first approach to the subject, renowned relativist James Hartle provides a fluent and accessible introduction that uses a minimum of new mathematics and illustrates a wealth of applications. Recognizing that there is typically not enough time in a short introductory course for the traditional, math-first, approach to the subject, Hartle presents a physics-first introduction to general relativity that begins with the essential physical applications.

Problem Book in Relativity and Gravitation

Author: Alan P. Lightman,William H. Press,Richard H. Price,Saul A. Teukolsky

Publisher: Princeton University Press

ISBN: 1400889014

Category: Science

Page: 616

View: 4625

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.

Gravity

Author: H. J. Bellus

Publisher: Createspace Independent Publishing Platform

ISBN: 9781542726832

Category:

Page: 304

View: 7116

Your first love is nothing to joke about. It's powerful, overwhelming, and something that haunts you forever. When your first love is severed, you lose a piece of your soul. Your world shatters. My first love, Amos Marshall, left something behind for me. He promised me forever and gave that to me. It's the GRAVITY that keeps my universe held together. This natural phenomenon keeps me whole to move forward every single day of my life. Back in his hometown with a life-changing secret to reveal, the problem is I'm too greedy to give up the last piece of Amos that I hold dear. Gravitational attraction has a funny way of pulling new people into your life. It's unwanted, but the force is tenacious. Cub Stent storms into my life piecing together my secret. He fills dark mysterious holes that have been vacant for years. Does my heart have room for a second love? Only Gravity will know.

Introducing Einstein's Relativity

Author: Ray D'Inverno

Publisher: Peterson's

ISBN: 9780198596868

Category: Science

Page: 383

View: 4617

There is little doubt that Einstein's theory of relativity captures the imagination. Not only has it radically altered the way we view the universe, but the theory also has a considerable number of surprises in store. This is especially so in the three main topics of current interest that this book reaches, namely: black holes, gravitational waves, and cosmology. The main aim of this textbook is to provide students with a sound mathematical introduction coupled to an understandingof the physical insights needed to explore the subject. Indeed, the book follows Einstein in that it introduces the theory very much from a physical point of view. After introducing the special theory of relativity, the basic field equations of gravitation are derived and discussed carefully as a prelude to first solving them in simple cases and then exploring the three main areas of application. Einstein's theory of relativity is undoubtedly one of the greatest achievements of the humanmind. Yet, in this book, the author makes it possible for students with a wide range of abilities to deal confidently with the subject. Based on the author's fifteen years experience of teaching this subject, this is achieved by breaking down the main arguments into simple logical steps. The book includes numerous illustrative diagrams and exercises (of varying degrees of difficulty), and as a result this book makes an excellent course for any student coming to the subject for the first time.