Module overview
This is a module principally on Einstein's general theory of relativity, a relativistic theory of gravitation which explains gravitational effects as coming from the curvature of space-time. It provides a comprehensive introduction to material which is currently the subject of enthusiastic study from the theoretical and experimental standpoints.
The module starts by introducing the special theory of relativity in a manner designed to make the transition to the general theory more tractable. In addition, in order to understand the general theory fully, some familiarity with tensor calculus is required. This will involve some self-study material at the start of the module. The rest of the module will be devoted to a detailed investigation of the theory itself together with applications to classical black holes and cosmology. The theory is full of surprises and challenging new ideas and the module is designed to make these accessible to students from a wide variety of backgrounds.
Linked modules
Pre-requisites: MATH2038 OR MATH2015 OR MATH2047 OR MATH2048
Aims and Objectives
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- Understand the key properties of black holes
- Solve Einstein's equations in a variety of simple situations
- Draw diagrams to explain many of the key properties of these solutions
- Appreciate the experimental status of the theory and derive the classic tests
- Understand the physical principles which guided Einstein to the theory of relativity
- Derive the basic results in cosmology
- Investigate the geodesic structure of the most important solutions of the theory
- Manipulate tensors in a competent manner
Syllabus
Introduction to tensors
Tensor algebra
Tensor calculus
Special Relativity
The key attributes of special relativity
The elements of relativistic mechanics
The principles of general relativity
Mach's principle
The principle of equivalence
The principle of general covariance
The simplicity principle
The correspondence principle
The field equations of general relativity
The energy-momentum tensor
Relativistic fluids
Experimental tests of general relativity
The Schwarzschild solution
The four classic tests
Geodesic motion
Classical black holes
Non-rotating black holes
Rotating black holes
Gravitational waves
Cosmology
Relativistic cosmology
Hubble's law
Classification and properties of Friedmann models
Learning and Teaching
Teaching and learning methods
Lectures, tutorials, private study
| Type | Hours |
|---|---|
| Lecture | 36 |
| Tutorial | 12 |
| Independent Study | 90 |
| Total study time | 138 |
Resources & Reading list
Textbooks
Schutz B.F, A. First Course in General Relativity. Cambridge University Press.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Written assessment | 50% |
| Coursework | 50% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Written assessment | 100% |
Repeat Information
Repeat type: Internal & External