Topics in the foundations of general relativity and Newtonian Gravitation Theory

Preface; 1. Differential Geometry; 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. Classical Relativity Theory; 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.
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