
The students will become familiar with:
 Causal theory of spacetimes, culminating in the notion of global hyperbolicity (in various equivalent forms)
 The singularity theorems of Hawking and Penrose
 Null geometry and Penrose diagrams
 Exact black hole solutions: Schwarzschild, ReissnerNordström, Kerr, and their (mathematical) properties
 Abstract theory of black holes
 The 3+1 split of general relativity and associated firstorder form of the Einstein equations
 Asymptotically flat spacetimes and the notion of mass


The content of this course consists of the list of aims.
Instructional Modes: This course consist of weekly lectures and problem classes led by a TA

 
This course is intended for master's students in mathematics, theoretical physics, or astronomy, such as those taking the Gravity+ synergy track, with a good bachelorlevel course in differential geometry and a first course in general relativity behind them. In particular, students should be familiar with such notions as: differentiable manifolds, tangent and cotangent bundles, vector fields, differential forms, tensors, Lie derivative, metric, LeviCivita connection, geodesics, curvature, Riemann tensor (these notions can also be picked up from the lecture notes but at very high speed). From basic general relativity it is mostly some intuition that should already be there, including a first familiarity with the Einstein equations and some exact solutions such as FriedmanLemaitreRobertsonWalker and Schwarzschild (although the latter will be redone in detail).

  


  Required materialsReaderKlaas Landsman, Foundations of General Relativity: From Geodesics to Black Holes 
Title  :   Foundations of General Relativity: From Geodesics to Black Holes 
Author  :   Klaas Landsman 
Publisher  :   Radboud University Press 
Edition  :   1 
Costs  :   0.00 

 Recommended materialsBookEric Poisson, A relativist's toolkit: The mathematics of blackhole mechanics 
ISBN  :   9780521537803 
Title  :   A relativist's toolkit: The mathematics of blackhole mechanics 
Author  :   Eric Poisson 
Publisher  :   Cambridge University Press 
Edition  :   1 
Costs  :   60.00 

 Instructional modesCourse GeneralPrecise course schedule is depending on the number of participants, but in any case a mixture of lectures, guided self study, and exercise class.

 TestsTentamenTest weight   1 
Opportunities   Block KW4, Block KW4 


 