ABOUT THIS BOOK

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. Topics is 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.

REVIEWS

“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 Malament’s treatment of them is extremely thorough and careful throughout. I thoroughly enjoyed reading this book.”

— David Garfinkle, Oakland University

“Recommended.”

— N. Sadababd, Central Connecticut State University, Choice

“Any mathematically sophisticated student or researcher interested in the foundations of gravitational theory and/or any of the specific applications would benefit from reading this book.”

— Deborah Konkowski, Zentralblatt MATH

"Malament’s lucid and thorough exposition is addressed both to philosophically inclined mathematical physicists and to philosophers of science with a strong mathematical and physical background. In fact, despite the book’s rather heavy mathematical demands, the latter will find philosophical excitement hidden behind lines."

— Theophanes Grammenos, Metascience

"Lucid and thorough. . . . Will open the way for even more researchers to consider the rich set of ideas examined here."

— John Byron Manchak, Philosophy of Science

TABLE OF CONTENTS

Contents

Preface

1.1 Manifolds

1.2 Tangent Vectors

1.3 Vector Fields, Integral Curves, and Flows

1.4. Tensors and Tensor Fields on Manifolds

1.5. The Action of Smooth Maps on Tensor Fields

1.6. Lie Derivatives

1.7. Derivative Operators and Geodesics

1.8. Curvature

1.9. Metrics

1.10 Hypersurfaces

1.11 Volume Elements

2.1 Relativistic Spacetimes

2.2 Temporal Orientation and “Causal Connectibility”

2.3 Proper Time

2.4 Space/Time Decomposition at a Point and Particle Dynamics

2.5 The Energy-Momentum Field Tab

2.6 Electromagnetic Fields

2.7 Einstein’s Equation

2.8 Fluid Flow

2.9 Killing Fields and Conserved Quantities

2.10 The Initial Value Formulation

2.11 Friedmann Spacetimes

3.1 Gödel Spacetime

3.2 Two Criteria of Orbital (Non-) Rotation

3.3 A No-Go Theorem about Orbital (Non-) Rotation

4. Newtonian Gravitation Theory

4.1 Classical Spacetimes

4.2 Geometrized Newtonian Theory—First Version

4.3 Interpreting the Curvature Conditions

4.4 A Solution to an Old Problem about Newtonian Cosmology

4.5 Geometrized Newtonian Theory—Second Version

Solutions to Problems

Bibliography

Index

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