Mathematical Introduction To General Relativity A Second Edition
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A Mathematical Introduction To General Relativity
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Author : Amol Sasane
language : en
Publisher: World Scientific
Release Date : 2021-08-10
A Mathematical Introduction To General Relativity written by Amol Sasane and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-10 with Science categories.
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 the (over 200) exercises are included.
Mathematical Introduction To General Relativity A Second Edition
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Author : Amol Sasane
language : en
Publisher: World Scientific
Release Date : 2024-12-20
Mathematical Introduction To General Relativity A Second Edition written by Amol Sasane and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-20 with Science categories.
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.
A First Course In General Relativity
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Author : Bernard Schutz
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-14
A First Course In General Relativity written by Bernard Schutz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-14 with Science categories.
Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.
A First Course In General Relativity
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Author : Bernard F. Schutz
language : en
Publisher: Cambridge University Press
Release Date : 1985-01-31
A First Course In General Relativity written by Bernard F. Schutz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-31 with Science categories.
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.
An Introduction To General Relativity
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Author : L. P. Hughston
language : en
Publisher: Cambridge University Press
Release Date : 1990
An Introduction To General Relativity written by L. P. Hughston and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.
The Geometry Of Minkowski Spacetime
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Author : Gregory L. Naber
language : en
Publisher: Courier Corporation
Release Date : 2003-01-01
The Geometry Of Minkowski Spacetime written by Gregory L. Naber and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
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.
The Geometry Of Spacetime
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Author : James J. Callahan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Geometry Of Spacetime written by James J. Callahan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
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.
General Relativity
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Author : Norbert Straumann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-09
General Relativity written by Norbert Straumann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-09 with Science categories.
This book provides a completely revised and expanded version of the previous classic edition ‘General Relativity and Relativistic Astrophysics’. In Part I the foundations of general relativity are thoroughly developed, while Part II is devoted to tests of general relativity and many of its applications. Binary pulsars – our best laboratories for general relativity – are studied in considerable detail. An introduction to gravitational lensing theory is included as well, so as to make the current literature on the subject accessible to readers. Considerable attention is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel’s proof of his uniqueness theorem, and a derivation of the basic laws of black hole physics. Part II ends with Witten’s proof of the positive energy theorem, which is presented in detail, together with the required tools on spin structures and spinor analysis. In Part III, all of the differential geometric tools required are developed in detail. A great deal of effort went into refining and improving the text for the new edition. New material has been added, including a chapter on cosmology. The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It utilizes a very well structured approach, which should help it continue to be a standard work for a modern treatment of gravitational physics. The clear presentation of differential geometry also makes it useful for work on string theory and other fields of physics, classical as well as quantum.
Math Intro Gen Relativ 2nd Ed Hb
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Author : AMOL. SASANE
language : en
Publisher: World Scientific Publishing Company
Release Date : 2024-12-30
Math Intro Gen Relativ 2nd Ed Hb written by AMOL. SASANE and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-30 with Science categories.
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.
Introduction To General Relativity And Cosmology
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Author : Christian G Boehmer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-10-06
Introduction To General Relativity And Cosmology written by Christian G Boehmer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-06 with Science categories.
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.