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# General Relativity - MAT00046M

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• Department: Mathematics
• Module co-ordinator: Dr. Daniel Siemssen
• Credit value: 10 credits
• Credit level: M
• Academic year of delivery: 2019-20

## Related modules

• None

### Prohibited combinations

• None

From 2019/20:

Classical Mechanics & Relativity with Professional Skills PHY00018C and Applied Mathematics for Mathematics & Physics MAT00039I

Or

Advanced Theoretical Techniques & Introduction to Quantum Computing PHY00044H and Relativity & Particle Physics PHY00042H

## Module will run

Occurrence Teaching cycle
A Autumn Term 2019-20

## Module aims

• To give an introduction to Einstein's general relativistic theory of gravitation.

• To explain how it provides a more accurate and satisfactory description of gravity than the Newtonian theory.

• To describe several or all of the following topics: tests of general relativity, black holes, cosmology.

## Module learning outcomes

• Appreciate the splendour of Einstein's achievement.

• Understand the reasons for supposing that gravity may be modelled in terms of a curved space-time.

• Appreciate how the differential geometry of surfaces in three dimensions may be generalised to give a theory of an -dimensional curved space with metric, and to understand those parts of Riemannian geometry and the tensor calculus needed to follow the arguments leading to Einstein's equations.

• Understand the conditions under which Einstein's theory reduces to the Newtonian Theory as a first approximation.

• Solve the Einstein equations for a static and bounded spherically symmetric distribution of matter leading to the Schwarzchild exterior metric.

• Appreciate (as time allows) formulas for the perihelion advance of planetary orbits, the deflection of light rays and the gravitational red shift, black holes, features of simple cosmological models.

## Module content

Syllabus

• A brief survey of the Newtonian theory of gravitation and the reasons for generalising the theory of special relativity in order to account for gravity.

• The idea that the paths of free particles or light rays are time-like or null geodesics, respectively, in a curved space-time.

• An introduction to Riemannian geometry, based on a metric as a generalisation of the differential geometry on a curved surface in three dimensions.

• Tensors and the tensor calculus.

• The Einstein field equation.

• The Schwarzchild metric.

• A selection of: the advance of the perihelion of planetary orbits, the deflection of light rays and the gravitational red shift; black holes; the application of general relativity to cosmology; gravitational radiation.

## Assessment

Task Length % of module mark
24 hour open exam
General Relativity
2 hours 100

None

### Reassessment

Task Length % of module mark
24 hour open exam
General Relativity
2 hours 100

## Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.