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Unit information: General Relativity and Cosmology in 2021/22

Unit name General Relativity and Cosmology
Unit code PHYSM1900
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Professor. Birkinshaw
Open unit status Not open

Relevant third year physics units.



School/department School of Physics
Faculty Faculty of Science

Description including Unit Aims

This unit gives an introduction to the General Theory of Relativity and, via differential geometry, derives the equations governing the behaviour of matter and radiation in the Universe. Cosmological models based on Einstein's field equations will be described and their observable consequences discussed. Recent developments in dark matter and dark energy are discussed. Black holes and gravitational radiation are also described and key results are derived.


  • To provide a physical understanding of the General Theory of Relativity, to demonstrate how to apply the theory to the Universe, compact objects, and gravitational radiation.
  • To make students familiar with the use of curved space-time in cosmology and astrophysics, and to enable them to calculate the observable consequences of relativistic gravitation.

Intended Learning Outcomes

Students will be able to

  • Describe the limitations of Newtonian gravity, and use the principle of equivalence to calculate redshifts
  • Make calculations using relativistic four-vectors and tensors and use metric tensors in calculations of relativistic invariants
  • Describe the role of the stress-energy tensor and its properties in Special Relativity
  • Derive the Friedmann-Robertson-Walker (FRW) solutions of Einstein's equations and show how these lead to different histories of the Universe
  • Show how the properties of geodesics in FRW metrics lead to observable redshifts, and the concepts of different distance measures
  • Reproduce the derivation of Hubble's law
  • Describe how to measure cosmological parameters
  • Work with other metrics, such as the weak field metric and the Schwarzschild metric
  • Discuss recent developments in cosmology in terms of dark matter and dark energy
  • Understand the nature of gravitational radiation in the weak-field limit.

Teaching Information

The unit will be taught through a combination of

  • asynchronous online materials, including narrated presentations and worked examples
  • synchronous group problems classes, workshops, tutorials and/or office hours
  • asynchronous directed individual formative exercises and other exercises
  • guided, structured reading

Assessment Information

30% of unit mark for mid-term short take-home essay, 70% examination.


If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. PHYSM1900).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.