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PX436-15 General Relativity

Undergraduate Level 4
Module leader
Gareth Alexander
Credit value
Module duration
10 weeks
100% exam
Study location
University of Warwick main campus, Coventry
Introductory description

Einstein's general theory of relativity (GR) is the basis for our understanding of black holes and the Universe on its largest scales. In GR the Newtonian concept of a gravitational force is abolished, to be replaced by a new notion, that of the curvature of space-time. This leads in turn to predictions of phenomena such as the bending of light and gravitational time dilation that are well tested, and others, such as gravitational waves, which have only recently been directly detected.

The module starts with a recap of Special Relativity, emphasizing its geometrical significance. The formalism of curved coordinate systems is then developed. Einstein's equivalence principle is used to link the two to arrive at the field equations of GR. The remainder of the module looks at the application of general relativity to stellar collapse, neutron stars and black-holes, gravitational waves, including their detection, and finally to cosmology where the origin of the "cosmological constant" - nowadays called "dark energy" - becomes apparent.

Module web page

Module aims

To present the theory of General Relativity and its applications in modern astrophysics, and to give an understanding of black-holes

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The geometry of space-time and the invariant “interval” in special relativity; geodesics and equations of motion applied to circular orbits within the Schwarzschild metric; 4-vector formulation of special relativity; metric of special relativity; the equivalence principle and local inertial frames; motivation for considering curved space-time; vectors and tensors in curved coordinate systems; geodesic motion revisited; motion in almost-flat space-time: the Newtonian limit; the curvature and stress-energy tensors; how the metric is determined: Einstein's field equations; Schwarzschild metric; observable consequences; black-holes; stability of orbits; extraction of energy; gravitational radiation and its detection; cosmology: the Robertson-Walker metric

Learning outcomes

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

  • Explain the metric nature of special and general relativity, how the metric determines the motion of particles
  • Undertake calculations involving the Schwarzschild metric
  • Describe features of black-holes
  • Demonstrate knowledge of current attempts to detect gravitational waves
Indicative reading list

BF Schutz A first course in general relativity, Cambridge University Press,
M.P Hobson, G. Efstathiou, A.N. Lasenby, General Relativity - An Introduction for Physicists, CUP,
L. D. Landau, E. M. Lifshit︠s︡, The Classical Theory of Fields

View reading list on Talis Aspire


The theory of General Relativity, like quantum theory, has been the result of collaboration between people working in physics and in mathematics with insights flowing in both directions. At its core is a simple hypothesis about observations (the equivalence principle), which leads to a theory of gravity based on the differential geometry of curved spaces. This module covers the necessary mathematics and computes some of the consequences of the theory for the physical Universe.

Subject specific skills

Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.

Transferable skills

Analytical, communication, problem-solving, self-study

Study time

Type Required
Lectures 30 sessions of 1 hour (20%)
Seminars (0%)
Private study 120 hours (80%)
Total 150 hours
Private study description

Self study


No further costs have been identified for this module.

You must pass all assessment components to pass the module.

Assessment group B2
Weighting Study time
On-campus Examination 100%

Answer 3 questions

  • Answerbook Pink (12 page)
  • Students may use a calculator
Feedback on assessment

Personal tutor, group feedback

Past exam papers for PX436


This module is Optional for:

  • TMAA-G1PE Master of Advanced Study in Mathematical Sciences
    • Year 1 of G1PE Master of Advanced Study in Mathematical Sciences
    • Year 1 of G1PE Master of Advanced Study in Mathematical Sciences
  • Year 1 of TMAA-G1P9 Postgraduate Taught Interdisciplinary Mathematics
  • Year 1 of TMAA-G1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
  • Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
  • Year 1 of TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
  • Year 4 of UPXA-F304 Undergraduate Physics (BSc MPhys)
  • Year 4 of UPXA-F303 Undergraduate Physics (MPhys)

This module is Option list A for:

  • Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
  • Year 3 of UMAA-G100 Undergraduate Mathematics (BSc)
  • Year 4 of UMAA-G101 Undergraduate Mathematics with Intercalated Year

This module is Option list B for:

  • Year 4 of UPXA-FG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
  • Year 4 of UPXA-FG31 Undergraduate Mathematics and Physics (MMathPhys)

This module is Option list C for:

  • UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
    • Year 3 of G105 Mathematics (MMath) with Intercalated Year
    • Year 5 of G105 Mathematics (MMath) with Intercalated Year
  • UMAA-G103 Undergraduate Mathematics (MMath)
    • Year 3 of G103 Mathematics (MMath)
    • Year 4 of G103 Mathematics (MMath)
  • UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
    • Year 3 of G106 Mathematics (MMath) with Study in Europe
    • Year 4 of G106 Mathematics (MMath) with Study in Europe