Homepage of Mathematics for General Relativity

Home page for

3305: Mathematics for General Relativity (2009)

7.10: Introduction to course. Definition of a manifold. Examples of surfaces and manifolds.
9.10: Definition of (0,1)-tensor. Einstein summing convention.
14.10: Definition of (1,0)-tensor, scalar, and (p,q)-tensor. Operations on tensors.
16.10: Vector analysis in R³.
21.10: Curves on manifolds, tangent vector to curves, length of (tangent) vector, metric tensor, signature, line element.
23.10: General comments on metric tensor. Length does not depend on coordinates.
28.10: Raising and lowering indices, definition of geodesics.
30.10: Geodesic equation in local coordinates. Definition of Christoffel symbols.
4.11: Examples of geodesics, Special relativity, inertial frame, Lorentz transformations
6.11: Lorentz transformations cont., Minkowski metric, time-, space-, and light-like curves.
9-13.11: reading week.
18.11: Time dilation, proper time, momentum and energy
20.11: rest energy, energy tensors
25.11: Covariant derivative, absolute derivative, Riemann curvature tensor
27.11: Symmetries of the Riemann curvature tensor
2.12: Geodesic deviation, Ricci curvature, scalar curvature, Einstein field equations
4.12: Einstein field equations
9.12: Postulate of GR, GR and Newton's first law, GR implies Newtonian gravity
11.12: GR implies Newtonian gravity (continued).
16.12: Geodesics of the Schwarzschild equation and light deflection

The course has ended. For my current contact information, see my homepage.

Solution available to instructors on request.

Grading: 90% by final exam and 10% by coursework. In computing the final coursework score, the exercise with lowest score will be discarded.