General Relativity (160243-WS 24/25)

Please register for this course in eCampus. You will then shortly receive access to the Moodle course ‘General Relativity’.

The lecture will take place in presence.

Literature: Sean Carroll: Spacetime and Geometry, Cambridge (2019) [Link to Errata und short summary]

free script: https://arxiv.org/abs/gr-qc/9712019 

The class will cover topics like:

SRT
tensors, field strength tensor, energy momentum tensor, manifolds, charts, atlas
vectors again, tensors, commutator, partial derivative on manifolds; expanding universe
causality, tensor densities, differential forms, wedge product, exterior derivative, cohomology, Hodge duality, Maxwell eqns as forms, integration
covariant derivative, parallel transport, geodesics
properties of geodesics, exponential map, Riemann normal coordinates
energy momentum tensor for expanding universe, Riemann curvature tensor
properties of the Riemann tensor, local and global symmetries, Ricci-, Weyl-, Einstein-tensor, symmetries and Killing vectors, Killing eqn.
Killing vectors and conserved current, Killing vectors of two sphere, maximally symmetric spaces in Euklidean and Minkowski signatures (spheres and hyperboloids, de Sitter, anti de Sitter), relation between geodesics and Newton
Lagrangian formulation, properties of the field equations, Planck numbers, cosmological constant
alternative theories
Schwarzschild
Singularities; geodesics in Schwarzschild
Perihelion rotation, redshift; The Schwarzschild manifold, Kruskal diagrams, wormholes
conformal transformations --> Penrose diagrams
conformal transformations --> optical geometry of space
More general black holes, event horizons, singularity theorems
Killing horizon, ergosphere
Mass, charge, spin
Charged (Reissner-Nordström) black holes
Rotating (Kerr) black holes
Gravitational waves
Cosmology