Undergraduate Course: Geometry of General Relativity (MATH11138)
Course Outline
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 closedbook 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, LeviCivita connection, curvature tensors, isometries, Killing vector fields.
General Relativity: special relativity and Minkowski spacetime, Maxwell's equations, postulates of General Relativity, spacetime, general covariance, energymomentum tensor, Einstein equations.
Schwarzschild solution: static and spherically symmetric spacetimes, derivation, black hole.

Information for Visiting Students
Prerequisites  Required knowledge may be deduced from the course descriptions and syllabuses of the prerequisite University of Edinburgh courses listed above.

High Demand Course? 
Yes 
Course Delivery Information

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  
Learning Outcomes
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.

Reading List
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) 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  GGR 
Contacts
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 

