Undergraduate Programme and Module Handbook 2024-2025

# Module MATH4051: GENERAL RELATIVITY IV

## Department: Mathematical Sciences

### MATH4051: GENERAL RELATIVITY IV

Type | Open | Level | 4 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | Location | Durham |
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#### Prerequisites

- Analysis in Many Variables II (MATH2031) AND ( Mathematical Physics II (MATH2071) OR Foundations of Physics 2A (PHYS2581) ) AND a minimum of 40 credits of Mathematics modules at Level 3.

#### Corequisites

- None.

#### Excluded Combination 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

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 42 | 2 per week for 20 weeks and 2 in term 3 | 1 Hour | 42 | |

Problems Classes | 8 | Four in each of terms 1 and 2 | 1 Hour | 8 | |

Preparation and Reading | 150 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

three hour written examination | 100% |

#### Formative Assessment:

Eight assignments to be submitted.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University