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General Relativity

A Geometric Approach

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Paperback | 4 October 1999

At a Glance

Paperback
230 Pages

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24.41 x 16.99 x 1.22

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Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. This allows the theory to be pared down and presented in its simplest and most elegant form. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. In developing the theory, all physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas in the text are illustrated with worked examples. Solutions and hints to selected problems are also provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity, and all the necessary mathematical machinery.

Industry Reviews

' ... written for final-year undergraduates mathematics or physics students ... This short, elegant book describes the major ideas of special and general relativity with unprecedented clarity and mathematical depth.' Physics Today 'Ludvigsen's book provides us with an elegant modern introduction to Einstein's general relativity; it is comprehensive, brief and very readable.' Professor Sir Roger Penrose, Mathematical Institute, University of Oxford ' ... a clear, clean, concise introduction to mathematical general relativity. It is a pleasure to see so many important topics discussed with such economy and care.' Professor Bernard F. Schutz, Max Planck Institute for Gravitational Physics, Potsdam 'The author has done a good work. The book is pedagogic and reads easily ... this book is recommended for undergraduate studies both in physics and in mathematics and also for faculty libraries ...'. A. F. Ranada, European Journal of Physics '... the book introduces many refreshing novelties to the subject ... Malcolm Ludvigsen's book is never dull and this is a major thing in its favour'. Graham S. Hall, General Relativity and Gravitation

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You Can Find This Book In

Non-Fiction Science Physics Relativity Physics Mathematics Applied Mathematics Astronomy, Space & Time Cosmology & The Universe

Preface	p. xi
The Concept of Spacetime	p. 1
Introduction	p. 3
Exercises	p. 11
Events and Spacetime	p. 12
Events	p. 12
Inertial Particles	p. 13
Light and Null Cones	p. 15
Exercises	p. 17
Flat Spacetime and Special Relativity	p. 19
Flat Spacetime	p. 21
Distance, Time, and Angle	p. 21
Speed and the Doppler Effect	p. 23
Exercises	p. 26
The Geometry of Flat Spacetime	p. 27
Spacetime Vectors	p. 27
The Spacetime Metric	p. 28
Volume and Particle Density	p. 35
Exercises	p. 38
Energy	p. 40
Energy and Four-Momentum	p. 41
The Energy-Momentum Tensor	p. 43
General States of Matter	p. 44
Perfect Fluids	p. 47
Acceleration and the Maxwell Tensor	p. 48
Exercises	p. 50
Tensors	p. 51
Tensors at a Point	p. 51
The Abstract Index Notation	p. 56
Exercises	p. 59
Tensor Fields	p. 61
Congruences and Derivations	p. 62
Lie Derivatives	p. 64
Exercises	p. 67
Field Equations	p. 69
Conservation Laws	p. 69
Maxwell's Equations	p. 70
Charge, Mass, and Angular Momentum	p. 74
Exercises	p. 78
Curved Spacetime and Gravity	p. 79
Curved Spacetime	p. 81
Spacetime as a Manifold	p. 81
The Spacetime Metric	p. 85
The Covariant Derivative	p. 86
The Curvature Tensor	p. 89
Constant Curvature	p. 93
Exercises	p. 95
Curvature and Gravity	p. 96
Geodesics	p. 96
Einstein's Field Equation	p. 99
Gravity as an Attractive Force	p. 103
Exercises	p. 105
Null Congruences	p. 106
Surface-Forming Null Congruences	p. 106
Twisting Null Congruences	p. 109
Exercises	p. 113
Asymptotic Flatness and Symmetries	p. 115
Asymptotically Flat Spacetimes	p. 115
Killing Fields and Stationary Spacetimes	p. 122
Kerr Spacetime	p. 126
Energy and Intrinsic Angular Momentum	p. 131
Exercises	p. 133
Schwarzschiid Geometries and Spacetimes	p. 134
Schwarzschild Geometries	p. 135
Geodesics in a Schwarzschild Spacetime	p. 140
Three Classical Tests of General Relativity	p. 143
Schwarzschild Spacetimes	p. 146
Exercises	p. 150
Black Holes and Singularities	p. 152
Spherical Gravitational Collapse	p. 152
Singularities	p. 155
Black Holes and Horizons	p. 158
Stationary Black Holes and Kerr Spacetime	p. 160
The Ergosphere and Energy Extraction	p. 167
Black-Hole Thermodynamics	p. 169
Exercises	p. 171
Cosmology	p. 173
The Spacetime of the Universe	p. 175
The Cosmological Principle	p. 175
Cosmological Red Shifts	p. 177
The Evolution of the Universe	p. 179
Horizons	p. 180
Exercises	p. 181
Relativistic Cosmology	p. 182
Friedmann Universes	p. 185
The Cosmological Constant	p. 186
The Hot Big-Bang Model	p. 187
Blackbody Radiation	p. 188
The Origin of the Background Radiation	p. 191
A Model Universe	p. 191
Exercises	p. 195
Solutions and Hints to Selected Exercises	p. 197
Bibliography	p. 213
Index	p. 215
Table of Contents provided by Syndetics. All Rights Reserved.

General Relativity

A Geometric Approach

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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