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General Relativity - MAT00089M

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  • Department: Mathematics
  • Module co-ordinator: Prof. Chris Fewster
  • Credit value: 20 credits
  • Credit level: M
  • Academic year of delivery: 2023-24
    • See module specification for other years: 2024-25

Module summary

General Relativity (GR) is the extension of Einstein’s theory of Special Relativity to incorporate gravity, which is now understood as the effect of spacetime curvature rather than a force as such. This module will explain General Relativity and its mathematical background, i.e., the calculus of tensors on manifolds. Various applications and consequences of GR will be studied, including black holes, gravitational waves and cosmology. Developments in these areas have produced a number of Nobel Prizes in recent years.

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Additional information

An introduction to General Relativity, its mathematical underpinnings and physical applications. Elective/MSc students should have studied Lagrangian mechanics and special relativity and have a firm background in mathematics applied to physics, preferably including the use of index notation and tensors in special relativity or other branches of mechanics.

Pre-requisite modules:

Electromagnetism & Special Relativity (H) or Quantum Field Theory (M)
Classical Dynamics (I)
Vector & Complex Calculus (I)

Post-requisite modules:

Advanced Mathematical Physics

 

 

Module will run

Occurrence Teaching period
A Semester 2 2023-24

Module aims

General Relativity (GR) is the extension of Einstein’s theory of Special Relativity to incorporate gravity, which is now understood as the effect of spacetime curvature rather than a force as such. This module will explain General Relativity and its mathematical background, i.e., the calculus of tensors on manifolds. Various applications and consequences of GR will be studied, including black holes, gravitational waves and cosmology. Developments in these areas have produced a number of Nobel Prizes in recent years.

Module learning outcomes

By the end of the module, students will be able to:

  1. Employ tensor calculus and index notation accurately;

  2. Solve unseen problems in General Relativity, including problems related to the geometry of curved manifolds, geodesics, tensor calculus and solutions of the Einstein equation;

  3. Interpret mathematical results concerning General Relativity in physical terms and vice versa.

Module content

  • 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.

  • An introduction to geometry of Riemannian and Lorentzian manifolds

  • Tensors and the tensor calculus.

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

  • The Einstein field equation and its Newtonian limit

  • The Schwarzschild metric

  • Gravitational waves

  • Cosmology

Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
General Relativity		 3 hours 100

Special assessment rules

None

Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
General Relativity		 3 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

SM Carroll, Spacetime and geometry: an introduction to general relativity

Cambridge University Press (U 0.11 CAR)

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

W Rindler, Essential relativity : special, general and cosmological, Springer (U 0.11 RIN)


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.