MATH40820: General Relativity

• Analysis in Many Variables and Mathematical Physics.

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

• 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.

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.

• 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.

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

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