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Basic general relativity corresponding to the last three chapters of the book “Semi-Riemannian Geometry” by Barrett O'Neill.
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Witten's as well as Schoen and Yau's proof of the positive mass theorem.
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The Yamabe problem.
FSF3671 Semi-riemannian Geometry 2 7.5 credits
Information per course offering
Course offerings are missing for current or upcoming semesters.
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus FSF3671 (Spring 2019–)Content and learning outcomes
Course contents
Intended learning outcomes
After the course, the student should have a sufficiently deep knowledge of semi-riemannian geometry to be able to work on research projects in the areas of in the areas of mathematical general relativity, positive mass theorems, the Yamabe problem.
Literature and preparations
Specific prerequisites
Prerequisite for the course is strong knowledge of semi-Riemannian geometry corresponding for example to the gradute level course SF3670 “Semi-Riemannian geometry 1”.
Recommended prerequisites
Equipment
Literature
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O'Neill, B. “Semi-Riemannian Geometry With Applications to Relativity”, Academic Press, Orlando 1983.
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Schoen, R; Yau, S.-T. “Lectures on differential geometry”. Conference Proceedings and Lecture Notes in Geometry and Topology, I. International Press, Cambridge, MA, 1994.
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Chrúsciel, P. T. “Lectures on Mathematical Relativity Beijing, July 2006”, lecture notes.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- HEM1 - Home assignments, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Homework assignments and oral test or presentation.
Other requirements for final grade
Homework assignments completed, and satisfactory performance at oral test or presentation.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.