This course is an introduction to the modern theory of classical gravity.
Generalizing from special relativity, we show the need for and will develop the formalism of differential geometry. This will allow us to study the motion of particles and fields in a gravitational field as motion through a curved spacetime. In turn this leads to the introduction of the Einstein field equations for the dynamics of the spacetime itself. Using these insights, we will study a variety of important physical consequences and applications, i.e. relativistic corrections to the Newtonian gravity, relativistic stars, gravitational waves, black holes and spacetime singularities, relativistic Big Bang cosmology. The course concludes with an outlook towards a quantum theory of gravity.
• Vectors, Tensors, Metrics and Manifolds (Riemannian geometry of curved spaces)
• Einstein’s General Theory of Relativity
• Energy theorems and singularities
• Schwarzschild solution and simple black holes
• Gravitational Waves
• Friedmann-Robertson-Walker Cosmology
• Towards astrophysics, the Big Bang and our Universe
2×2 hrs/week lectures for 8 weeks; 6 weekly problem sets
Lectures, problem sessions
S. Carroll, Spacetime and Geometry: An Introduction to General Relativity; Benjamin Cummings, 2003
Form of examination
60% Problem assignments; 40% Written Final exam (must pass