Lecturers: Dr. Christopher Moore (part I), Dr. Davide Gerosa (part II) and Dr. Patricia Schmidt (part III)
Start: 1/10/2020
Thursdays 2:00-3:00
Zoom link will be circulated by email.
There will be nine 1 hour lectures spread throughout the term. The course will conclude with a 1 day residential workshop in Birmingham which will elaborate on some of the topics covered with practical numerical calculations performed using Python.
Prerequisites: General knowledge of tensor and vector calculus at the level of a typical undergraduate course will be assumed. A basic knowledge of the Python language is required for the 1 day workshop at the end of the course (if the students have no previous python experience they could attend the Python MPAGS course which runs concurrently with this course).
The first module will give an overview of some of the mathematical background to general relativity: manifolds, the metric, tensors, covariant derivatives, the Riemannian curvature. We will then cover the linearised Einstein field equations and the Schwarzschild solution.
This module covers the basics of gravitational wave emission and propagation: linearization of the Einstein field equations, their Newtonian limit, and the gravitational-wave quadrupole formula. We then apply this formalism to the specific case of binary black holes and highlight their astrophysical relevance.
This part of the course will give a basic introduction to numerical relativity - the field of solving Einstein’s field equations numerically. We will cover the 3+1 decomposition of the field equations, briefly introduce gauge conditions and initial data for black hole spacetimes, before looking at the evolution of black hole spacetimes and gravitational wave extraction.
The course will conclude with an interactive, hands-on workshop, which will provide provide a taste of current gravitational-wave data-analysis methods.
The course will be assessed via 3 short example sheets (one for each part of the course) which students can complete in their own time and submit online to the lecturer.
Please upload your problem sheets at https://forms.gle/mCBFAfGAvU8V4Ke16
Materials from previous editions remains available in dedicated branches of this repository.
