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MATH4051: GENERAL RELATIVITY IV

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Type	Open
Level	4
Credits	20
Availability	Available in 2023/24
Module Cap
Location	Durham
Department	Mathematical Sciences

Prerequisites

Analysis in Many Variables II (MATH2031) AND ( MathematicalPhysics II (MATH2071) OR Foundations of Physics 2A (PHYS2581) ) 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 physicaltheories.
To develop and exercise mathematical methods.

Content

Differences between general and special relativity.
Gravity becomes geometry.
Differential manifold as model ofspacetime.
Coordinates and relations between differentsystems.
Covariant derivative.
Geodesic curves.
Metric connection.
Distance relations, shape, units, light cones, locallyinertial coordinate systems.
Variational principles for geodesics.
Curvature tensor.
Symmetries of curvature tensor.
Einstein tensor.
Geodesic deviation.
Newtonian gravity and Einstein'stheory.
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 solvecomplex, unpredictable and specialised problems in GeneralRelativity.
have an understanding of specialised and complex theoreticalmathematics in the field of General Relativity.
have mastered a coherent body of knowledge of these subjectsdemonstrated 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 advancedmathematical skills which will be used with minimal guidance in thefollowing 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 theapplication of the theory to practical examples.
Formatively assessed assignments provide practice in theapplication of logic and high level of rigour as well as feedback forthe students and the lecturer on students' progress.
The end-of-year examination assesses the knowledge acquiredand the ability to solve complex and specialised problems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total
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 written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

More information

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