Topics in the Foundations of General Relativity and Newtonian Gravitation Theory

by Malament, David B.

• ISBN13: 9780226502458
• ISBN10: 0226502457
• Format: Hardcover
• Copyright: 2012-05-07
• Publisher: Univ of Chicago Pr

Summary

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 Gödel 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. Topicsis intended for both students and researchers in mathematical physics and philosophy of science.

Author Biography

David B. Malament is professor in the Department of Logic and Philosophy of Science at the University of California, Irvine. He is the editor of Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics.

Table of Contents

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
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