Convenor: Christopher Moore C.J.Moore@bham.ac.uk and Patricia Schmidt

Module Code: GW

Module Name: Black Hole and Gravitational Waves

Start Date and Commitments

Not running 2024/25

Once registered the module convenor will be in contact with online access details

Material:

https://github.com/dgerosa/mpags_blackholesgravitationalwaves

Module Details

 

 

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).

 

Course Outline:

 

Part I: Christopher Moore Lectures 1-3

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 Einstein field equations and the Schwarzschild solution.

 

Part II: Davide Gerosa Lectures 4-6

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.

 

Part III: Patricia Schmidt Lectures 7-9

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.

 

 

Assessment: 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.