Faculty of Science

Riemannian Geometry and General Relativity
Provider: Faculty of Science

Activity no.: 5548-19-07-31
	Enrollment deadline: 02/09/2019

Place

Department of Mathematical Sciences

Date and time

02.09.2019, at: 09:00 - 10.11.2019, at: 16:00

Regular seats

ECTS credits

7.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Bergfinnur Durhuus E-mail address: durhuus@math.ku.dk

Written language

English

Teaching language

English

Semester/Block

Block 1

Scheme group

Exam form

Continuous assessment

Exam form

Continuous assessment

Exam details

The 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 category	Hours
Preparation	106.00
Exam	28.00
Lectures	40.00
Theory exercises	32.00

Sum	206.00

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.

Click the search button to search Courses.

See which courses you can attend and when

Jan	Feb	Mar	Apr
May	Jun	Jul	Aug
Sep	Oct	Nov	Dec