General relativity

Course goals

1. understands the concepts of Riemann spaces and metric tensor, and has notions of Levi-Civita connection, geodesic equation and space-time curvature
2. can relate Killing vectors and tensors to conservation laws; can write down Einstein's field equations and derive their weak field limit
3. understands the properties of black hole space-times; has notion of conformal diagrams of some space-times
4. knows basic cosmological space times and their properties, and knows of tests of general relativity
5. knows how can we `see' the Universe by using gravitational waves

Content

This course is an introduction to the theory of General Relativity at an advanced level. Its aim is to convey the fundamental geometric concepts of the theory and the techniques required to express them quantitatively. We will study a number of important physical phenomena for which general relativity provides a theoretical description, including gravitational radiation, black holes and cosmological applications.