An introduction to xAct with applications to metric-affine gravity, cosmology and black holes.

4-4-4426 - Seminari Física Teòrica (Campus Burjassot)

4-4-4426 - Seminari Física Teòrica

Campus Burjassot


Schedule: Four sessions of 2 hours each on April 11,12, and 13 from 11:00 to 13:00 plus one more lecture on Tuesday 12 in the afternoon. 

Lecturer: Jose Beltrán Jiménez (U. Salamanca, Spain). 


The goal of the course will be to give an elementary and practical introduction to the Mathematica package xAct ( The philosophy of the lectures will be to get familiarised with some capabilities of the packages by working out explicit problems. Some basic notions of Mathematica would be desirable. Basics of field theory, gravitation, cosmology and black holes physics will also be helpful, but not strictly necessary. As a matter of fact, the proposed problems aim at providing some basics of cosmological perturbations, gravitational waves oscillations and black hole perturbations physics.


Lecture I (2 hours): First steps with xAct

I.1.- Installation, general philosophy of the package and survey of the different capabilities.

I.2.- Defining manifolds, metrics, connections and tensors.

I.3.- Proving some Bianchi identities.

I.4.- Some applications in field theory: Computing field equations and the energy-momentum tensor.


Lecture II (2 hours): Application to cosmological perturbations.

II.1.- Working with charts.

II.2.- Gauge transformations.

II.3.- Weinberg theorem: Conservation of adiabatic modes.


Lecture III (2 hours): Application to oscillations of gravitational waves.

III.1 Inequivalent realisations of the cosmological principle. Working with two manifolds.

III.2 Isotropic solutions with SU(2) cosmological fields.

III.3. Two tensor modes: Oscillations of gravitational waves.


Lecture IV (2 hours): Applications to black holes.

IV.1. Spherically symmetric solutions.

IV.2. Perturbations of black holes.

IV.3. Vanishing Love numbers.

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