General Relativity - MAT00046M

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  • Department: Mathematics
  • Module co-ordinator: Prof. Atsushi Higuchi
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2019-20

Module summary

From 2019/20:

Applied stream MAT00034I, MAT00036I, or MAT0037I

Or

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

Or

Advanced Theoretical Techniques PHY00007H and Special and General Relativity PHY00017H

 

Related modules

Co-requisite modules

  • None

Prohibited combinations

  • None

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
University - closed examination
General Relativity
2 hours 100

Special assessment rules

None

Reassessment

Task Length % of module mark
University - closed examination
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.

Indicative reading

M Ludvigsen, General Relativity: a geometric approach, Cambridge University Press (S.82 LUD).



The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.