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MATH4051: General Relativity IV

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Type Open
Level 4
Credits 20
Availability Available in 2025/2026
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • Analysis in Many Variables II (MATH2031) AND ( Mathematical Physics II (MATH2071) OR Theoretical Physics 2 (PHYS2631) ) AND a minimum of 40 credits of Mathematics modules at Level 3.

Corequisites

  • None.

Excluded Combinations of Modules

  • None.

Aims

  • To appreciate General Relativity, one of the fundamental physical theories.
  • To develop and exercise mathematical methods.

Content

  • Differences between general and special relativity.
  • Gravity becomes geometry.
  • Differential manifold as model of spacetime.
  • Coordinates and relations between different systems.
  • Covariant derivative.
  • Geodesic curves.
  • Metric connection.
  • Distance relations, shape, units, light cones, locally inertial coordinate systems.
  • Variational principles for geodesics.
  • Curvature tensor.
  • Symmetries of curvature tensor.
  • Einstein tensor.
  • Geodesic deviation.
  • Newtonian gravity and Einstein's theory.
  • Linear form of Einstein's theory.
  • Schwarzschild solution, black holes.
  • Cosmology.

Learning Outcomes

Subject-specific Knowledge:

  • By the end of the module students will:
  • be able to solve complex, unpredictable and specialised problems in General Relativity.
  • have an understanding of specialised and complex theoretical mathematics in the field of General Relativity.
  • have mastered a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas:
  • Special relativity.
  • Differential manifolds.
  • Metric, covariant derivative, curvature.
  • General relativity.
  • Black holes.
  • Cosmology.

Subject-specific Skills:

  • Students will have highly specialised and advanced mathematical skills which will be used with minimal guidance in the following areas: Geometrical awareness, Modelling.

Key Skills:

  • Students will have enhanced problem solving skills.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
  • Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
  • The end-of-year examination assesses the knowledge acquired and the ability to solve complex and specialised problems.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures422 per week for 20 weeks and 2 in term 31 Hour42 
Problem Classes8Four in each of terms 1 and 21 Hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
On Campus Written Examination3 hours100

Formative Assessment

Eight assignments to be submitted.

More information

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