Undergraduate Programme and Module Handbook 2009-2010 (archived)

Module MATH3331: GENERAL RELATIVITY III

Department: Mathematical Sciences

MATH3331: GENERAL RELATIVITY III

Type	Open	Level	3	Credits	20	Availability	Available in 2009/10 and alternate years thereafter	Module Cap	None.	Location	Durham

Prerequisites

Linear Algebra II (MATH2021), Analysis in Many Variables II (MATH2031) and Mathematical Physics II (MATH2071); alternatively Linear Algebra II (MATH2021), Analysis in Many Variables II (MATH2031) and Foundations of Physics II (PHYS2511).

Corequisites

None.

Excluded Combination of Modules

General Relativity IV (MATH4051).

Aims

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

Content

(1) Difference between general and special relativity.
Experiments showing up the differences.
Gravity becomes geometry.
(2) Differential manifold as model of spacetime.
Coordinates and relations between different systems.
Curves in spacetime.
(3) Covariant derivative.
Partial derivatives are inadequate.
Properties (linearity, derivative of tensor product, commutation with contraction).
Geodesic curves.
Metric connection.
(4) Distance relations, shape units, light cones, locally inertial coordinate systems.
Variational principles for geodesics.
(5) Curvature tensor.
Symmetries of curvature tensor.
Einstein tensor.
Geodesic deviation.
(6) Newtonian gravity and Einstein's Theory.
Linear form of Einstein's theory.
(7) Schwarzschild solution, blackholes with Kruskal-Szekeres coordinates.
(8) 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 ares: spatial 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.
Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
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 predictable and unpredictable problems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total/Hours
Lectures	40	2 per week for 19 weeks and 2 in term 3	1 hour	40
Preparation and Reading				160
Total				200

Summative Assessment

Component: Examination		Component Weighting: 100%
Element	Length / duration	Element Weighting	Resit Opportunity
three-hour written examination	3 hours	100%

Formative Assessment:

Four written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

■ 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