Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer and they contain proofs of the results from the class notes. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors). These notes are based on Chapter 2 of Hawking and Ellis's The Large Scale Structure of Space-Time.

Chapter 2. Differential Geometry.

• Section 2.1. Manifolds (Partial). Section 2.1 notes
• Supplement. Proofs of Theorems in Section 2.1. Beamer file of Section 2.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section 2.1. Print file of Section 2.1 proofs
• Section 2.2. Vectors and Tensors.
• Section 2.3. Maps of Manifolds.
• Section 2.4. Exterior Differentiation and the Lie Derivative.
• Section 2.5. Covariant Differentiation and the Curvature Tensor.
• Section 2.6. The Metric.
• Section 2.7. Hypersurfaces.
• Section 2.8. The Volume Element and Gauss' Theorem.
• Section 2.9. Fibre Bundles.
• Study Guide 2.

Additional Chapters.

• Chapter 1. The Role of Gravity.
• Chapter 3. General Relativity.
• Chapter 4. The Physical Significance of Curvature.
• Chapter 5. Exact Solutions.
• Chapter 6. Causal Structure.
• Chapter 7. The Cauchy Problem in General Relativity.
• Chapter 8. Space-Time Singularities.
• Chapter 9. Gravitational Collapse and Black Holes.
• Chapter 10. The Initial Singularity in the Universe.

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