PX4124: Introduction to General Relativity
| School | Cardiff School of Physics & Astronomy |
| Department Code | PHYSX |
| Module Code | PX4124 |
| External Subject Code | 100425 |
| Number of Credits | 10 |
| Level | L7 |
| Language of Delivery | English |
| Module Leader | PROFESSOR Mark Hannam |
| Semester | Autumn Semester |
| Academic Year | 2015/6 |
Outline Description of Module
To provide an introduction to the physical concepts of general relativity, with applications to spherical stars, black holes and gravitational waves.
On completion of the module a student should be able to
The student will be able to:
Describe the principle of relativity and its implications for Newtonian mechanics and electromagnetism.
Describe the equivalence principle and how gravity can be interpreted as the curvature of spacetime.
Describe the four basic tests of general relativity (perihelion precession of Mercury, bending of light by the sun, Shapiro time delay, and gravitational redshift).
Write down and solve the geodesic equation in some simple cases.
Write down and interpret the metric outside a spherical star or black hole.
Derive the potential that governs the trajectory of a particle or light ray in the Schwarzschild geometry and solve for the trajectory in some simple cases.
Explain how the Schwarzschild geometry acts as a black hole.
Compute lengths, areas, and volumes and perform basic vector operations in curved spacetimes.
How the module will be delivered
Lectures 22 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 - Autumn Semester | 80 | Introduction To General Relativity | 2 |
| Written Assessment | 20 | Introduction To General Relativity | N/A |
Syllabus content
Introduction: Importance of gravitational physics. Geometry as physics. Space and time in Newtonian physics. Principle of relativity. Variational principle.
Review of special relativity: Fundamental postulates. Lorentz transformation. Spacetime diagrams. Minkowski metric. 4-vectors. Light rays. Proper time.
Gravity as geometry: Equivalence principle. Gravitational redshift. Description of curved spacetime. Metric. Vectors. Geodesics.
Spherical Stars: Schwarzschild geometry. Gravitational redshift. Trajectories of particles and light.
Schwarzschild black holes: Eddington-Finkelstein coordinates. Kruskal-Szekeres coordinates.
Background Reading and Resource List
An Introduction to Einstein’s General Relativity, J B Hartle (Addison Wesley, 2003) ISBN 0-8053-8662-9