After completing the course the student shall be able to
explain and describe the equivalence principle,
explain the concept of a metric and solve geodesic equations,
analyse and solve Einstein's equations for many situations,
explain what a black hole is and describe its properties,
describe the concepts within the standard cosmological model, such as the expanding universe, the cosmic microwave background radiation, dark matter as well as inflation.
The course is an introduction to general relativity with applications to cosmology. Connections with modern research are emphasised throughout the course in order to bring the student up to date with the scientific frontline. The first part of the course introduces general relativity; its mathematical basis in the form of Einstein's equations and the mathematics of curved space-time, metrics, curvature tensors and geodesics; the equivalence principle; classical tests of the theory such as the bending of light and the precession of the perihelion of Mercury; gravitational waves. The mathematical description of black holes in the form of the Schwarzchild metric with an analysis of its horizon and singularity. Kerr and Reissner-Nordström black holes. The course's second part treats applications within cosmology. The mathematical description of the Robertson-Walker metric, the Big Bang, the expanding universe with a cosmological constant, dark matter, the cosmic microwave background radiation and inflation will be analysed and discussed.
Lectures and lessons.
Written examination at the end of the course combined with hand-in problems during the course.
week 02, 2018
Carroll, Sean M.
Spacetime and geometry : an introduction to general relativity