Login for PhD students/staff at UCPH      Login for others
Riemannian Geometry and General Relativity
Provider: Faculty of Science

Activity no.: 5548-19-07-31 
Enrollment deadline: 02/09/2019
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time02.09.2019, at: 09:00 - 10.11.2019, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserBergfinnur Durhuus    E-mail address: durhuus@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 1
Scheme groupC
Exam formContinuous assessment
Exam formContinuous assessment
Exam detailsThe grade will be based on two major assignments to be completed in weeks 5 and 9, respectively. In addition, one must either hand in 5 smaller assignments in weeks 2,3,4,6,7 or give a seminar talk of 45 minutes about a topic to be specified during the course. If one or more of the minor assignments have not been accepted (i.e. are at least 50% correct) or the seminar talk is not deemed acceptable, the student will receive the grade -3.
Course workload
Course workload categoryHours
Preparation106.00
Exam28.00
Lectures40.00
Theory exercises32.00
Sum206.00
Content
1. Differentiable manifolds and vector bundles.

2. Linear connections and curvature tensor

3. Riemannian metric, the Levi-Civita connection and the Einsten equation

4. Causal structure, causality conditions and global hyperbolicity

5. Extremal properties of geodesics

6. Singularity theorems or gravitational waves

Learning outcome
At the end of the course the students are expected to have acquired the following knowledge and associated tool box:
the mathematical framework of (semi-)Riemannian geometry, including the Levi-Civita connection and the Riemann curvature
the mathematical formulation of General Relativity, including causal structure, global hyperbolicity and the Einstein equation
fundamental properties of solutions to Einstein's equations: singularity theorems or wave properties.


Skills:
be able to work rigorously with problems from Riemannian geometry
be able to work rigorously with problems from General Relativity
be able to use extremal properties of geodesics to analyse singularity properties of solutions to Einstein's equation or else characterise and possibly establish existence of wave type solutions

Competences: The course aims at training the students in representing, modelling and handling physical problems of general relativity by mathematical concepts and techniques.

Literature
Lecture notes and possibly some selected articles.

Teaching and learning methods
Lectures and tutorials:
3+2 lectures (including possible seminars by students) and 2+2 tutorials per week during 8 weeks.

Search
Click the search button to search Courses.


Course calendar
See which courses you can attend and when
JanFebMarApr
MayJunJulAug
SepOctNovDec



Publication of new courses
All planned PhD courses at the PhD School are visible in the course catalogue. Courses are published regularly.