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MC435 General Relativity

MC435 General Relativity

Credits: 20 Convenor: Dr. M. D. Dampier Semester: 2
Prerequisites: essential: MC224, MC227 or MC256
Assessment: Regular coursework: 10% Three hour exam: 90%
Lectures: 36 Problem Classes: 10
Tutorials: none Private Study: 104
Labs: none Seminars: none
Project: none Other: none
Surgeries: none Total: 150

Course Description

The general theory of relativity is one of the greatest achievements of scientific thought and remains one of our fundamental tools for understanding the physical universe. Founded in 1915 by Einstein, the theory develops the idea of special relativity to include situations where gravitation becomes important and and leads to some of the most surprising results of twentieth century science. The course develops the theory using classical mathematical tools. (Students taking the Differential Geometry module MC442 will find that the General Relativity course complements it well.)

Aims

This course aims to provide an understanding of the basic principles of the theory and the ability to use those principles to solve problems. It is also an aim that at the end of the course student will be in a position to read advanced texts in the subject and be in a position to pursue postgraduate studies in the field including its astrophysical applications.

Objectives

To be able to use the geometrical ideas of curvature and geodesics to solve problems relevant to the theory of general relativity. To be able to use the Schwarzschild and other metrics to solve problems involving particle orbits and light rays. To be able to solve simple problems on free fall, collapse, and black holes. To be able to use the Robertson-Walker metrics to discuss simple cosmological ideas.

Syllabus

1. Founding the theory: space-time, curvature, gravitation.
2. Testing the theory: spherical symmetry, planetary motion, light rays.
3. Using the theory: black holes, the expanding universe, the 'big bang'.

Transferable Skills

Understanding and being able to use the geometrical approach to modelling real world problems. Problem solving in applied mathematical contexts.

Reading list

Recommended:

J.Foster and J.D.Nightingale, Short course in General Relativity, Springer.

Background:

D.J.Raine, The Isotropic Universe, Adam Hilger.

Details of Assessment

The final assessment of this module will consist of 10% coursework and 90% from a three hour examination during the Summer exam period. The 10% coursework contribution will be determined by students' solutions to coursework problems. The examination paper will contain 6 questions with full marks on the paper obtainable from 4 complete answers.

Next: MC442 Differential Geometry Up: Year 4 Previous: MC434 Time Dependent Partial Differential Equations

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Last updated: 2001-09-20
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