PX4224: Advanced General Relativity and Gravitational Waves
| School | Cardiff School of Physics & Astronomy |
| Department Code | PHYSX |
| Module Code | PX4224 |
| External Subject Code | 100415 |
| Number of Credits | 10 |
| Level | L7 |
| Language of Delivery | English |
| Module Leader | Dr Frank Ohme |
| Semester | Spring Semester |
| Academic Year | 2015/6 |
Outline Description of Module
To provide a thorough introduction to the theory of general relativity, with applications to gravitational waves.
To develop skills in the use of tensor calculus and differential geometry.
On completion of the module a student should be able to
Carry out basic operations on tensor and tensor components (e.g. addition and subtraction, inner and outer products, contraction, transformation of tensor components, covariant derivatives, parallel transport).
Compute the curvature tensor, Ricci tensor, curvature scalar, and Einstein tensor given the metric of a spacetime.
Write down and interpret the Einstein equation.
Describe the basic properties of gravitational waves.
Compute the gravitational-wave luminosity for some simple sources, such as a compact binary system or rotating ellipsoidal body.
Describe how an interferometric gravitational-wave antenna functions, and the limiting noise sources for ground-based and space-based detectors.
Describe the basic principles of gravitational-wave detection by pulsar timing.
Describe expected sources of gravitational waves for ground-based and space-based detectors and pulsar timing arrays.
How the module will be delivered
Lectures 22 x 1 hr, Exercises 11 x 1 hr.
Skills that will be practised and developed
Problem solving. Investigative skills. Mathematics. Analytical skills.
How the module will be assessed
Examination and Continuous Assessment
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Exam - Spring Semester | 80 | Advanced General Relativity And Gravitational Waves | 2 |
| Written Assessment | 20 | Advanced General Relativity And Gravitational Waves | N/A |
Syllabus content
Differential Geometry: Tensor algebra. Covariant derivative. Riemann curvature tensor.
Differential Geometry: Geodesic deviation. Vacuum Einstein equation.
Gravitational waves: Linearized gravity and gravitational waves.
Sources of curvature: Stress-energy tensor. Conservation of energy-momentum. Production of gravitational waves. Quadrupole formula.
Evidence of gravitational waves: Hulse-Taylor binary pulsar.
Detecting gravitational waves: Laser interferometers. Noise sources.
Gravitational waves: CMB polarisation.
Detecting gravitational waves: Pulsar timing arrays. Noise sources.
Gravitational-wave sources: Compact binary coalescence.
Gravitational-wave sources: Gamma-ray bursts, supernovae. Pulsars.
Gravitational-wave sources: Stochastic backgrounds.
Gravitational-wave astronomy: Cosmology from standard sirens. Testing general relativity.
Background Reading and Resource List
An Introduction to Einstein’s General Relativity, J B Hartle (Addison Wesley, 2003) ISBN 0-8053-8662-9