This course is being taught in parallel at the following universities:
Lectures take place online in BigBlueButton and are recorded. Recordings can be found under the same link (a few hours after the lecture). Lecture times in autumn / winter semester 2020 / 2021:
UTC | CET (Germany) | EET (Estonia) | |
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Mondays | 14:15 - 15:45 | 15:15 - 16:45 | 16:15 - 17:45 |
Thursdays | 10:15 - 11:45 | 11:15 - 12:45 | 12:15 - 13:45 |
First lecture: | October 26th, 2020 |
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Last lecture: | December 17th, 2020 |
There will be a final seminar for students to get credit points for the course. Talks are supposed to be 10-15 minutes + 5 minutes for questions and can be on any topic related to perturbation theory and gravity. Based on the answers from the poll, the final seminar will take place on Monday, January 4th, 2021, at the usual time of the Monday lecture.
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.
Topic | Mathematica notebook | |
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Linear perturbations around a general metric and Minkowski background | MetricPerturb.nb | MetricPerturb.pdf |
Newtonian limit, Poisson equation, Euler equations of fluid dynamics | - | to come |
Linearized vacuum Einstein equations, harmonic gauge, plane gravitational waves | - | LinearWave.pdf |
Emission of gravitational waves in linearized general relativity, quadrupole formula, symmetric binary | - | WaveGen.pdf |
Lorentz transformation, Newman-Penrose formalism, polarization of gravitational waves in general relativity and beyond | - | NewmanPenrose.pdf |
Linear perturbations around a Friedmann-Lemaître-Robertson-Walker background, vacuum Einstein equation for tensor perturbations | EinsteinCosmoTensor.nb | EinsteinCosmoTensor.pdf CosmoPerturb.pdf |
Gauge invariant linear cosmological perturbations in general relativity with fluid matter | CosmoGaugeTrans.nb | CosmoGaugeTrans.pdf CosmoPerturb2.pdf (to come) |
Perturbation of Schwarzschild spacetime and quasi-normal modes | SchwarzschildPerturb.nb | SchwarzschildPerturb.pdf |
Asymptotically flat spacetimes and the Bondi-Metzner-Sachs algebra | - | to come |
Higher order perturbations of the metric tensor and derived objects | MetricPerturb2.nb | MetricPerturb2.pdf |
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 |
Arbitrary order perturbations of Einstein's equations in the harmonic gauge | Harmonic.nb | Harmonic.pdf |
Higher order cosmological perturbations in general relativity | - | CosmoPerturb3.pdf (to come) |
Higher order gauge invariant perturbation theory | - | GaugeInvPerturb.pdf |
Perturbations of other fields - connection, tetrad, Finsler geometry | - | PerturbGeom.pdf |