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General Relativity (Springer Undergraduate Mathematics)

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Synopses & Reviews

Publisher Comments:

Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the "local inertial coordinates" set up by an observer in free fall, in which special relativity is valid over short times and distances. In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors. The basic theory is presented using techniques, such as phase-plane analysis, that will already be familiar to mathematics undergraduates, and numerous problems, of varying levels of difficulty, are provided to test understanding. The latter chapters include the theoretical background to contemporary observational tests - in particular the detection of gravitational waves and the verification of the Lens-Thirring precession - and some introductory cosmology, to tempt the reader to further study. While primarily designed as an introduction for final-year undergraduates and first-year postgraduates in mathematics, the book is also accessible to physicists who would like to see a more mathematical approach to the ideas.

Synopsis:

Based on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.

Synopsis:

Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the local inertial coordinates set up by an observer in free fall, in which special relativity is valid over short times and distances. In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors. The basic theory is presented using techniques, such as phase-plane analysis, that will already be familiar to mathematics undergraduates, and numerous problems, of varying levels of difficulty, are provided to test understanding. The latter chapters include the theoretical background to contemporary observational tests - in particular the detection of gravitational waves and the verification of the Lens-Thirring precession - and some introductory cosmology, to tempt the reader to further study. While primarily designed as an introduction for final-year undergraduates and first-year postgraduates in mathematics, the book is also accessible to physicistswho would like to see a more mathematical approach to the ideas.

About the Author

Nick Woodhouse is an experienced researcher in GR with an international reputation.

Table of Contents

Newtonian Gravity.- Inertial Coordinates and Tensors.- Energy-Momentum Tensors.- Curved Space-Time.- Tensor Calculus.- Einstein's Equation.- Spherical Symmetry.- Orbits in the Schwarzschild Space-Time.- Black Holes.- Rotating Bodies.- Gravitational Waves.- Redshift and Horizons.- Notes on the Exercises.- Further Problems.- Bibliography.- Index.

Product Details

ISBN:
9781846284861
Author:
Woodhouse, N. M. J.
Publisher:
Springer
Author:
Woodhouse, Nicholas
Subject:
Applied
Subject:
Mathematical Physics
Subject:
Geometry - Differential
Subject:
General relativity (physics)
Subject:
Mathematics-Applied
Subject:
Cosmological
Subject:
Curved space-time
Subject:
General relativity
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
Theoretical, Mathematical and Computational Physics
Subject:
Differential geometry
Subject:
Classical and Quantum Gravitation, Relativity Theory
Subject:
Astronomy, Astrophysics and Cosmology
Copyright:
Edition Description:
1st ed. 2007
Series:
Springer Undergraduate Mathematics Series
Publication Date:
20061115
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
230
Dimensions:
235 x 178 mm 910 gr

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Related Subjects

Health and Self-Help » Health and Medicine » Medical Specialties
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Geometry
Science and Mathematics » Physics » Math
Science and Mathematics » Physics » Relativity Theory

General Relativity (Springer Undergraduate Mathematics) New Trade Paper
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Product details 230 pages Springer - English 9781846284861 Reviews:
"Synopsis" by , Based on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.
"Synopsis" by , Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the local inertial coordinates set up by an observer in free fall, in which special relativity is valid over short times and distances. In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors. The basic theory is presented using techniques, such as phase-plane analysis, that will already be familiar to mathematics undergraduates, and numerous problems, of varying levels of difficulty, are provided to test understanding. The latter chapters include the theoretical background to contemporary observational tests - in particular the detection of gravitational waves and the verification of the Lens-Thirring precession - and some introductory cosmology, to tempt the reader to further study. While primarily designed as an introduction for final-year undergraduates and first-year postgraduates in mathematics, the book is also accessible to physicistswho would like to see a more mathematical approach to the ideas.
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