The course will be conducted in a hybrid format. The provided digital course materials are lecture notes and recorded video lectures (see below). These will be accompanied by classes taking place Mondays at 16:15 and Thursdays at 12:15 in Physicum room A111. In order to pass the course, please do the following for each of the 16 lectures:
The dates, lecture topics and questions are listed below.
Please click on 🎥 to watch the recorded lectures. To execute the Mathematica notebooks, you need the tensor algebra package suite xAct, for the cosmological perturbations also xPand and for the calculation of PPN parameters xPPN. Alternatively, there is also a PDF made from every Mathematica notebook.
No. | Date | 🎥 | Topic | Mathematica notebook | |
---|---|---|---|---|---|
1 | 24.10.2022 | 🎥 | Linear perturbations around a general metric and Minkowski background | MetricPerturb.nb | MetricPerturb.pdf |
2 | 27.10.2022 | 🎥 | Newtonian limit, Poisson equation, Euler equations of fluid dynamics | - | Newton.pdf |
3 | 31.10.2022 | 🎥 | Linearized vacuum Einstein equations, harmonic gauge, plane gravitational waves | - | LinearWave.pdf |
4 | 03.11.2022 | 🎥 | Emission of gravitational waves in linearized general relativity, quadrupole formula, symmetric binary | - | WaveGen.pdf |
5 | 07.11.2022 | 🎥 | Lorentz transformation, Newman-Penrose formalism, polarization of gravitational waves in general relativity and beyond | NewmanPenrose.nb | NewmanPenrose.pdf WavePol.pdf |
6 | 10.11.2022 | 🎥 | Linear perturbations around a Friedmann-Lemaître-Robertson-Walker background, vacuum Einstein equation for tensor perturbations | EinsteinCosmoTensor.nb | EinsteinCosmoTensor.pdf CosmoPerturb.pdf |
7 | 14.11.2022 | 🎥 | Gauge invariant linear cosmological perturbations, perturbed energy-momentum tensor | CosmoGaugeTrans.nb | CosmoGaugeTrans.pdf CosmoPerturb2.pdf |
8 | 17.11.2022 | 🎥 | Gauge invariant matter perturbations, perturbed Einstein equations with matter | ||
9 | 21.11.2022 | 🎥 | Perturbation of Schwarzschild spacetime and quasi-normal modes | SchwarzschildPerturb.nb | SchwarzschildPerturb.pdf |
10 | 24.11.2022 | 🎥 | Asymptotically flat spacetimes and the Bondi-Metzner-Sachs algebra | - | AsymptoticSym.pdf |
11 | 28.11.2022 | 🎥 | Higher order perturbations of the metric tensor and derived objects | MetricPerturb2.nb | MetricPerturb2.pdf |
12 | 01.12.2022 | 🎥 | Parametrized post-Newtonian formalism | - | PPN.pdf |
Post-Newtonian parameters for general relativity | GR.wl → PPN_GR.nb | PPN_GR.pdf | |||
Post-Newtonian parameters for scalar-tensor gravity | STG.wl → PPN_STG.nb | PPN_STG.pdf | |||
13 | 05.12.2022 | 🎥 | Arbitrary order perturbations of Einstein's equations in the harmonic gauge | Harmonic.nb | Harmonic.pdf |
14 | 08.12.2022 | 🎥 | Higher order cosmological perturbations in general relativity | CosmoGaugeTrans2.nb | CosmoGaugeTrans2.pdf |
15 | 12.12.2022 | 🎥 | Higher order gauge invariant perturbation theory | - | GaugeInvPerturb.pdf |
16 | 15.12.2022 | 🎥 | Perturbations of other fields - connection, tetrad, Finsler geometry | - | PerturbGeom.pdf |