Univ. Bremen
Prof. Dr. C. Lämmerzahl
Black Holes
(S3, elective, 6 ECTS)
Learning Outcomes:Students understand the physical and mathematical properties of Black Holes. They are able to calculate important effects relevant for observations, in particular related to light rays and
particle trajectories.
Knowledge and Understanding:

Applying Knowledge and Understanding:Participants understand the basic properties of Black Holes and the effects of particle and light motion in these Black Hole space-times with application to observations.
PrerequisitesBasic knowledge of General Relativity is beneficial
ProgramAfter a short repetition of the needed basics of General Relativity the following issues will be covered
– introduction of black hole solutions of the Einstein field equation (Schwarzschild, Kerr, etc)
– spherically symmetric Black Holes, uniqueness theorems
– introduction of various coordinate systems (e.g.
Eddington-Finkelstein, Kruskal-Szekeres)
– definition of event horizons
– definition of spherical and axial symmetries in space-times, Killing vectors
– analytical extension of Black Hole space-times
– effects on light rays and particle motion in Black Hole space-times
– Observation scenarios of Black Holes (e.g. via light effects, stellar orbits, shadows, gravitational waves, accretion disks)
Description of how the course is conducted– Contact hours (lecture + exercise): 56 h (4 h x 14 weeks)
– Preparation, learning, exercises: 56 h (4 h x 14 weeks)
– Preparation for exam: 68 h
Total working hours: 180 h
Description of the didactic methods
Description of the evaluation methodsWritten exam, oral exam, or study work
Adopted Textbooks– Ch. W. Misner, K. S. Thorne, and J.A. Wheeler:
Gravitation, Freeman and Co., San Francisco 1973
– I. Novikov and V. Frolov: Physics of Black Holes – Basic Concepts and New Developments, Springer Science and Business Media Dordrecht 1998.
– Additional literature will be announced in the course
Recommended readings