The University of Southampton
Courses

# MATH6107 Gravitational Waves

## Module Overview

This module is designed for MMath and MPhys students in their fourth year, and builds directly upon MATH3006 Relativity, Blackholes and Cosmology. Gravitational waves are tiny ripples in space-time, first predicted by Einstein himself in 1916. These "wrinkles in the spacetime curvature" carry information from the most violent events in the Universe - from colliding black holes, collapsing stars, to the birth of the Universe itself. Exactly one hundred years after Einstein’s prediction, after many decades of searching, scientists announced that they had finally detected these waves, from two black holes colliding at a distance of over one billion light years from Earth. This module aims to introduce you to the many issues involved in understanding gravitational waves and their generation from astrophysical sources. It will give you an insight into one of the hottest topics in modern research, and an insight into what has been described as the “greatest scientific achievement of the century.”

### Aims and Objectives

#### Module Aims

• to understand the physical nature of gravitational waves, as well as the mathematical tools used for investigating these waves; • to explore various astrophysical sources of gravitational waves; and • to appreciate various approximative and numerical methods used in modelling gravitational-wave sources.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Understand the nature of gravitational waves and issues regarding their detection
• Understand the basic ideas of the post-Newtonian approximation and relativistic perturbation calculations
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Give an oral presentation on an aspect of gravitational-wave theory studied during the course
• Write a report on an aspect of gravitational-wave theory studied during the course
• Solve relevant problems and motivate the answers in a clear way
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Obtain simple estimates for gravitational waves from various model sources

### Syllabus

Gravitational waves in the weak field approximation : • Using the TT gauge to understand gravitational waves • Energy carried by gravitational waves • Interaction of gravitational waves with detectors Wave generation and post-Newtonian approximation: • Mass- and current multipole radiation • Relativistic perturbation theory Astrophysical gravitational-wave sources : • Overview of detectable sources • Chirping binary systems (the quadrupole formula) • Tri-axial stars (pulsars and other spinning stars) • Oscillating stars

### Learning and Teaching

#### Teaching and learning methods

The lecturer will provide a structured week-by week programme of self-study, based mainly on printed notes, but with references to other material as appropriate. There will be one timetabled hour per week. In week 1 the lecturer will brief the students on the programme of study for the module. In subsequent weeks the students will be expected to meet by themselves, at a designated timetabled hour, for a self-study tutorial session. They will each take responsibility for leading the session, based on guidance from the lecturer given in the intial briefing, supplemented as necessary. There will be a subsequent timetabled office hour where the lecturer can be consulted. In addition a web-based bulletin board for the module will be set up, using the BLACKBOARD system. Towards the end of the module each student will be required to give a 20 minute presentation on some aspect of the subject. The students will be expected to agree the presentation topics between themselves, which some guidance from the lecturer, so as to minimise overlap between the presentations. The presentation will be assessed by the lecturer, using protocols developed in the department for presentation assessments. The presentation will contribute 20% to the assessment. An additional 20% will arise from a report on which the presentation is based. This report will normally contain more detail than will be possible in the oral presentation. The remaining assessment will be based on a portfolio of solved problems submitted periodically during the module. A high standard of explanation will be expected in the solutions, and this will form part of the assessment criteria in addition to their mathematical correctness and the scope of the problems submitted.

TypeHours
Independent Study126
Teaching24
Total study time150

SCHUTZ , B F,. A first course in General Relativity.

MISNER CW, THORNE K S, AND WHEELER J A. Gravitation.

D'INVERNO R,. Introduction to Einstein's Relativity.

### Assessment

#### Summative

MethodPercentage contribution
Oral presentation 20%
Portfolio of Problems 60%
Written report 20%

#### Referral

MethodPercentage contribution
Exam 100%

Pre-requisite: MATH3006

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.

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