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In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and G”del spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is no criterion of orbital rotation in general relativity that fully answers to our classical intuitions. Topics is intended for both students and researchers in mathematical physics and philosophy of science.
"This is a unique book by a talented author who spans the communities of general relativity and philosophy of science. The topics discussed are very interesting and cannot be found in other books on general relativity, and David B. Malament's treatment of them is extremely thorough and careful throughout. I thoroughly enjoyed reading this book." (David Garfinkle, Oakland University)"
| Preface | p. ix |
| Differential Geometry | p. 1 |
| Manifolds | p. 1 |
| Tangent Vectors | p. 7 |
| Vector Fields, Integral Curves, and Flows | p. 17 |
| Tensors and Tensor Fields on Manifolds | p. 24 |
| The Action of Smooth Maps on Tensor Fields | p. 35 |
| Lie Derivatives | p. 42 |
| Derivative Operators and Geodesies | p. 49 |
| Curvature | p. 68 |
| Metrics | p. 74 |
| Hypersurfaces | p. 94 |
| Volume Elements | p. 112 |
| Classical Relativity Theory | p. 119 |
| Relativistic Spacetimes | p. 119 |
| Temporal Orientation and "Causal Connectibility" | p. 128 |
| Proper Time | p. 136 |
| Space/Time Decomposition at a Point and Particle Dynamics | p. 140 |
| The Energy-Momentum Field Tab | p. 143 |
| Electromagnetic Fields | p. 152 |
| Einstein's Equation | p. 159 |
| Fluid Flow | p. 167 |
| Killing Fields and Conserved Quantities | p. 175 |
| The Initial Value Formulation | p. 181 |
| Friedmann Spacetimes | p. 183 |
| Special Topics | p. 195 |
| Gödel Spacetime | p. 195 |
| Two Criteria of Orbital (Non-)Rotation | p. 219 |
| A No-Go Theorem about Orbital (Non-)Rotation | p. 237 |
| Newtonian Gravitation Theory | p. 248 |
| Classical Spacetimes | p. 249 |
| Geometrized Newtonian Theory-First Version | p. 266 |
| Interpreting the Curvature Conditions | p. 279 |
| A Solution to an Old Problem about Newtonian Cosmology | p. 288 |
| Geometrized Newtonian Theory-Second Version | p. 296 |
| Solutions to Problems | p. 309 |
| Bibliography | p. 343 |
| Index | p. 347 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780226502458
ISBN-10: 0226502457
Series: Chicago Lectures in Physics
Audience:
Tertiary; University or College
Format:
Hardcover
Language:
English
Number Of Pages: 366
Published: 7th May 2012
Dimensions (cm): 23.2 x 15.5
x 2.547
Weight (kg): 0.612
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