A copy of the syllabus (handed out in class).
Course content
- Differential Geometry.
- Einstein equations.
- Solutions of the equations. Exact solutions.
Textbooks
The main sources for the course are:
- S. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge, 1973.
- D. Malament, Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, online notes, to apperar in Chicago Univ. Press, 2012.
Additional references:
- N. Straumann, General Relativity, with applications to Astrophysics Springer, 2004.
- R. Wald, General Relativity Chicago, 1984.
- N. M. J. Woodhouse, General Relativity Springer, 2007.
- C. Misner, K. Thorne, and J. A. Wheeler, Gravitation Freeman, 1973.
Differential Geometry is adequately covered in most of the above quoted references. Specific references, covering manifolds and their geometry from a modern point of view, are:
- I. M. Singer and J. A. Thorpe, Lecture Notes on Elementary Topology and Geometry Springer, 1976.
- S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces American Mathematical Society, 2001.
- J. Jost, Riemannian Geometry and Geometric Analysis Springer, 1995.
- B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity Academic Press, 1983