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Black Hole and Gravitational Waves

Convenor: Christopher Moore (module convenor; part I), Davide Gerosa (part II) and Patricia Schmidt (part III)

Module Code: GW

Module Name: Black Hole and Gravitational Waves

Start Date and Commitments

Start: 3/10/2019

End: 28/11/2019
Thursdays 2:00-3:00

Material:

https://github.com/dgerosa/mpags_blackholesgravitationalwaves

Module Details

 

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).

 

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.

 

Residential Workshop:

As this course will have remote participation, the workshop will provide the only opportunity to gather everyone together in one place. The workshop will take place over one day after the end of the autumn term. We plan to start at 10.00am and finish a 5.00 to accommodate people travelling to Birmingham (some financial support for travel will be available). There will be two sessions in which the students will work together to use python to solve a numerical exercise based one of the topics covered in the lectures. If possible students should bring their own laptops with a working Python installation (please let us know in advance if this is a problem and we will make alternative arrangements).

 

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.