Perturbative Methods in Gravity Theory (LTFY.04.011 / 5.04.4251)

General information

This course is being taught in parallel at the following universities:

Time and place


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)
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
Last lecture: December 17th, 2020

Students' seminar

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.

Course materials

Lecture notes

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 PDF
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
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.wlPPN_GR.nb PPN_GR.pdf
Post-Newtonian parameters for scalar-tensor gravity STG.wlPPN_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

Additional recommended literature

Links to computational tools