Univ. Bremen
Prof. C. Lämmerzahl
Advanced General Relativity
(S3, elective, 6 ECTS)
Learning Outcomes:
Knowledge and Understanding:

Applying Knowledge and Understanding:Participants understand the basic principles underlying Special Relativity and General Relativity and the theoretical predictions and the experimental schemes underlying the corresponding tests,
ProgramBased on the course “Introduction to General Relativity” more specialized issues which are of wider interest are will be treated. (i) At be beginning more general geometries (affine, Einstein-Cartan, with non-metricity) will be described. This is of importance for discussing generalized models of gravity as inspired by, e.g. quantum gravity. (ii) Then the theory of congruences will be introduced which has applications, e.g., in cosmology, star dynamics, and geodesy. (iii) The introduced notions will also be used in the derivation of the dynamics of extended objects, that is, of the Mathisson-Papapetrou equations. (iv) Related to that is the notion of multipoles of the gravitational field. These will be introduced and discussed. (v) Another important point is the solution of the Einstein equation. For obtaining analytical solutions the Ernst equation are derived from the Einstein equations in the case of stationary axially symmetric solutions. The Ernst equations can be solved for arbitrary axially symmetric multipole moments of the gravitational field introduced above. (vi) Furthermore, the first steps towards numerical relativity will be explained. For that, a 3+1 decomposition of space-time is introduced and the Einstein equations are split into dynamical equations and constraints.
Description of how the course is conducted
Description of the didactic methods
Description of the evaluation methods
Adopted TextbooksA list of references will be provided at the start of the semester.
Recommended readings