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Lorentzian geometry (Differential geometry III) Semester
WiSe 2021 / 22
Lecturer
Bernd Ammann
Type of course (Veranstaltungsart)
Vorlesung
German title
Lorentzsche Geometrie
Contents
In this lecture we want to deepen our knowledge about semi-Riemannian and in particular Lorentzian manifolds. The precise content will be fixed a bit later, but it is likely to be a choice out of the following:
- Where do the Einstein equations come from? The Einstein equations as stationary points of a variational problem
- gravitational waves
- special solutions of Einstein's equations, e.g. the Kerr solution for rotating black holes
- sagemath/python tools to do calculations in general relativity
- the positive mass theorem
- wave equations on Lorentzian manifolds, leading to quatization of fields
- solving the Einstein equations as a pde
- more about causality, Cauchy hypersurfaces, global hyperbolicity
Literature
- M. Kriele. Spacetime, Foundations of General Relativity
and Differential Geometry. Springer 1999
- B. O'Neill. Semi-Riemannian geometry. With applications to relativity.
Pure and Applied Mathematics, 103. Academic Press
- R. Wald. General Relativity. University of Chicago Press
- S. W. Hawking and G. F. R. Ellis. The large scale structure of space-time, Cambridge Monographs on Mathematical Physics, 1973
More literature will be announced during the lecture.
Recommended previous knowledge
Analysis I-IV, Lineare Algebra I+II,
differential geometry I. Helpful is the lecture differential geometry II, but as the topics are pretty disjoint, the gaps could be compensated by reading some literature.
Time/Date
Monday and Wednesday 8-10
Location
Mo M102. Wed M101
Course homepage
https://ammann.app.uni-regensburg.de/lehre/2021w_diffgeo3
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)
Registration- Registration for the exercise classes: Details will later be given on the homepage, please
register on GRIPS - Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)- Successful participation in the exercise classes: 50% of the points and one successful
presentation of the solution of an exercise
Examination (Prüfungsleistungen)- Oral exam: Duration: 30 min, Date: arranged individually, re-exam: Date:
Additional comments
Exercises will be organized, details will be announced later on the webpage.
Exercises are planned
for Tuesday16-18 in M101.
Modules
BV, MV, MGAGeo
ECTS
9
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