Mathematics Of Relativity
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Mathematical Problems Of General Relativity I
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Author : Demetrios Christodoulou
language : en
Publisher: European Mathematical Society
Release Date : 2008
Mathematical Problems Of General Relativity I written by Demetrios Christodoulou and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton's theory of gravitation as well as Newton's equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss' intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method, the study and systematic use of foliations by characteristic (null) hypersurfaces, is in the spirit of Roger Penrose's approach in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media. The book is intended for advanced students and researchers seeking an introduction to the methods and applications of general relativity.
The Geometry Of Spacetime
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Author : Rainer Oloff
language : en
Publisher: Springer Nature
Release Date : 2023-04-21
The Geometry Of Spacetime written by Rainer Oloff and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-21 with Science categories.
This book systematically develops the mathematical foundations of the theory of relativity and links them to physical relations. For this purpose, differential geometry on manifolds is introduced first, including differentiation and integration, and special relativity is presented as tensor calculus on tangential spaces. Using Einstein's field equations relating curvature to matter, the relativistic effects in the solar system including black holes are discussed in detail. The text is aimed at students of physics and mathematics and assumes only basic knowledge of classical differential and integral calculus and linear algebra.
Mathematics Of Relativity
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Author : George Yuri Rainich
language : en
Publisher: Courier Corporation
Release Date : 2014-11-19
Mathematics Of Relativity written by George Yuri Rainich and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Science categories.
Based on the ideas of Einstein and Minkowski, this concise treatment is derived from the author's many years of teaching the mathematics of relativity at the University of Michigan. Geared toward advanced undergraduates and graduate students of physics, the text covers old physics, new geometry, special relativity, curved space, and general relativity. Beginning with a discussion of the inverse square law in terms of simple calculus, the treatment gradually introduces increasingly complicated situations and more sophisticated mathematical tools. Changes in fundamental concepts, which characterize relativity theory, and the refinements of mathematical technique are incorporated as necessary. The presentation thus offers an easier approach without sacrifice of rigor. Dover (2014) republication of the edition published by John Wiley & Sons, New York, 1950. See every Dover book in print at www.doverpublications.com
General Relativity And The Einstein Equations
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Author : Yvonne Choquet-Bruhat
language : en
Publisher: OUP Oxford
Release Date : 2008-12-04
General Relativity And The Einstein Equations written by Yvonne Choquet-Bruhat and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-04 with Mathematics categories.
General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.
A Mathematical Journey To Relativity
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Author : Wladimir-Georges Boskoff
language : en
Publisher: Springer Nature
Release Date : 2020-06-01
A Mathematical Journey To Relativity written by Wladimir-Georges Boskoff and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-01 with Science categories.
This book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.
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.
Introduction To Mathematical Relativity
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Author : José Natário
language : en
Publisher:
Release Date : 2021
Introduction To Mathematical Relativity written by José Natário and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Electronic books categories.
This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics. It emerged from lecture notes originally conceived for a one-semester course in Mathematical Relativity which has been taught at the Instituto Superior Tecnico (University of Lisbon, Portugal) since 2010 to Masters and Doctorate students in Mathematics and Physics. Mostly self-contained, and mathematically rigorous, this book can be appealing to graduate students in Mathematics or Physics seeking specialization in general relativity, geometry or partial differential equations. Prerequisites include proficiency in differential geometry and the basic principles of relativity. Readers who are familiar with special relativity and have taken a course either in Riemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this book.
The General Theory Of Relativity
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Author : Anadijiban Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-26
The General Theory Of Relativity written by Anadijiban Das 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 2012-06-26 with Science categories.
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.
Mathematics Of Relativity Lecture Notes
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Author : George Yuri Rainich
language : en
Publisher: Forgotten Books
Release Date : 2015-06-12
Mathematics Of Relativity Lecture Notes written by George Yuri Rainich and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-12 with Science categories.
Excerpt from Mathematics of Relativity Lecture Notes Old Physics; Motion of a Particle. The Inverse Square Law; Two Pictures of Matter; Vectors, Tensors, Operations; Maxwell's Equations; The Stress-Energy Tensor; General Equations of Motion. The Complete Tensor; New Geometry; Analytic Geometry of Four Dimensions; Axioms of Four-Dimensional Geometry; Tensor Analysis; Complications Resulting From Imaginary Coordinate; Are the Equations of Physics Invariant; Curves in the New Geometry; Special Relativity; Equations of Motion; Lorentz Transformations; Addition of Velocities; Light Corpuscles, or Photons; Electricity and Magnetism in Special Relativity; Curved Space; Curvature of Curves and Surfaces; Generalizations; The Riemann Tensor; Vectors in General Coordinates; Tensors in General Coordinates; Covariant and Contravariant Components; Physical Coordinates as General Coordinates; Curvilinear Coordinates in Curved Space; New Derivation of the Riemann Tensor; Differential Relations for the Riemann Tensor; Geodesics; General Relativity; The Law of Geodesics; Solar System, Symmetry Conditions; Solution of the Field Equations; Equations of Geodesics; Newtonian Motion of a Planet; Relativity Motion of a Planet; Deflection of Light; Shift of Spectral Lines About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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.