# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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# Undergraduate Course: Geometry of General Relativity (MATH11138)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 11 (Year 5 Undergraduate) Availability Available to all students SCQF Credits 10 ECTS Credits 5 Summary Einstein's theory of General Relativity is a geometric theory of gravitation. This course is a modern introduction to this cornerstone of mathematical physics, formulated in the language of differential geometry. There are two lectures a week and a workshop every two weeks. There are biweekly assignments and a closed-book exam. Course description This course first develops all the differential geometry required to describe the theory of General Relativity. This includes differentiable manifolds, tensor calculus, affine connections, metric and curvature tensors. Then, the postulates of General Relativity and Einstein equations are presented in this language. The final part of the course is concerned with studying solutions to the Einstein equations, including the famous Schwarzschild solution and black hole. Syllabus: Manifolds and tensors: differentiable manifolds, tangent space, tensor algebra, vector and tensor fields, maps of manifolds, Lie derivative. Affine connections: covariant derivative, torsion, curvature, parallel transport, geodesics, geodesic deviation. Riemannian geometry: metric tensors, Lorentzian metrics, Levi-Civita connection, curvature tensors, isometries, Killing vector fields. General Relativity: special relativity and Minkowski spacetime, Maxwell's equations, postulates of General Relativity, spacetime, general covariance, energy-momentum tensor, Einstein equations. Schwarzschild solution: static and spherically symmetric spacetimes, derivation, black hole.
 Pre-requisites Students MUST have passed: Honours Algebra (MATH10069) AND Geometry (MATH10074) Co-requisites Prohibited Combinations Other requirements None
 Pre-requisites Required knowledge may be deduced from the course descriptions and syllabuses of the pre-requisite University of Edinburgh courses listed above. High Demand Course? Yes
 Academic year 2015/16, Available to all students (SV1) Quota:  None Course Start Semester 2 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 ) Assessment (Further Info) Written Exam 95 %, Coursework 5 %, Practical Exam 0 % Additional Information (Assessment) Coursework 5%, Examination 95% Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S2 (April/May) Geometry of General Relativity (MATH11138) 2:00
 On completion of this course, the student will be able to: State definitions and theorems and present standard proofs accurately without access to notes/books.Perform local calculations in differential geometry accurately (tensor calculus, covariant derivatives, Lie derivatives)Calculate curvature tensors for simple spacetimes.Derive and solve the geodesic equations for simple spacetimes.Apply theory developed in the course to solve unseen problems.
 Recommended: An Introduction to General Relativity, L.P Hughston and K.P. Tod (LMS, CUP, 1990) General Relativity, R. M. Wald, University of Chicago Press (1984)
 Graduate Attributes and Skills Not entered Keywords GGR
 Course organiser Dr James Lucietti Tel: (0131 6)51 7179 Email: J.Lucietti@ed.ac.uk Course secretary Mr Thomas Robinson Tel: (0131 6)50 4885 Email: Thomas.Robinson@ed.ac.uk
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