Blockseminar über Mathematische Relativitätstheorie

[W: 1; SSch: 2.1, 2.2, 5.1, 5.5, 6, 7, 9]The presentations not in bold are optional. Those in bold are essential. If we can’t find speakers for them, the lecturers will present them.

1. Physical Concepts I  [W: 1; SSch: 2.1, 2.2, 5.1, 5.5, 6, 7, 9]:
   Shane Farnsworth
   
   • Constancy of the speed of light, causality
   • Equivalence principle, the “Einstein elevator”
2. Effects of special relativity [W: 1, 2.3, 4.1,4.2, 8; S: 2.I; SSch: 5.4, 7, 9]:
   • Minkowski space, causal structure
   • Relativistic dynamics, the energy-momentum vector, $E=mc^2$
   • The twin paradox
3. Fundamentals of classical differential geometry I [W: 2, ; ON: 1, 2; N: 5, 7.1, 7.4; HE: 2]:
   Felix Finster
   • Riemannian and Lorentzian metrics
   • Geodesics, Levi-Civita connection
4. Fundamentals of Classical Differential Geometry II [W: 3.2; ON: 3; N: 7.3; S: 2.II.1; HE]:
   Sebastian Heiß
   • Riemann curvature tensor, Ricci tensor, scalar curvature
   • The Bianchi identities
5. The Einstein field equations and the Einstein-Hilbert action [W: 4.3, E ; HE: 3; S: 2.II ; BEE: 2.6]:
   Vincent Bäuml
   • Einstein’s field equations
   • Some basics of the calculus of variations
   • Derivation of Einstein’s field equations from the Einstein-Hilbert action
6. Special Solutions I: Schwarzschild Metric [W: 6; HE: 5.5 ;S: 2.III ;ON: 13 ; BE: 5.2]:
   Felix Finster
   • Schwarzschild metric
   • Event horizon, black holes
   • Redshift on the horizon
7. Penrose diagrams [HE; BEE]:
   • of Minkowski space
   • of Schwarzschild spacetime
   • optional: the Kruskal extension
8. Cosmological Spacetimes [W: 5 ; HE: 5.1-5.4 ; ON: 12 ; BEE: 5.4]:
   Anis Mokni
   
   • the Big Bang
   • The FLRW metric
9. Special Solutions II: Gravitational Waves [W: 4.4 ; S: 2.IV; BE]:
   Shane Farnsworth
   • Alternatively linearized gravity or as an exact solution
10.  Killing vectors [W:C; N: 7.7; HE: 2; ON: 9]: Alexander Koller
    • Symmetries of the metric, the Killing equation
    • Conservation quantities for geodesics and for the energy-momentum tensor
11. Special Solutions III: Kerr Metric [W: 12; HE: 5.6; BE: 5; S: 3.vii]:
    • rotating black holes, 
    • the Penrose process
12. Other physical field equations in curved spacetime:
    • scalar wave equation
    • Maxwell’s equations
13. Kaluza-Klein theory as a precursor to gauge theories
14. Global hyperbolic spacetimes [BEE; W; HE]:
    • normal-hyperbolic equations
15. The singularity theorems of Hawking and Penrose [W: 9; HE: 8; BE: 12]:
16. Spinors in curved spacetime: ZB [FKT: 4; W: 13; N: 7.10] 
    Jan Herzberg