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Course module: NWI-WM159
NWI-WM159
Singularities and Black Holes
Course infoSchedule
Course moduleNWI-WM159
Credits (ECTS)6
CategoryMA (Master)
Language of instructionEnglish
Offered byRadboud University Nijmegen; Faculty of Science; Wiskunde, Natuur- en Sterrenkunde;
Lecturer(s)
Coordinator
prof. dr. N.P. Landsman
Other course modules lecturer
Lecturer
prof. dr. N.P. Landsman
Other course modules lecturer
Contactperson for the course
prof. dr. N.P. Landsman
Other course modules lecturer
Examiner
prof. dr. N.P. Landsman
Other course modules lecturer
Academic year2021
Period
KW3-KW4  (31/01/2022 to 31/08/2022)
Starting block
KW3
Course mode
full-time
Remarks-
Registration using OSIRISYes
Course open to students from other facultiesYes
Pre-registrationNo
Waiting listNo
Placement procedure-
Aims
The students will become familiar with:
- Causal theory of space-times, 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, Reissner-Nordström, Kerr, and their (mathematical) properties
​- Abstract theory of black holes
- The 3+1 split of general relativity and associated first-order form of the Einstein equations
- Asymptotically flat space-times and the notion of mass
Content
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
Level

Presumed foreknowledge
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 bachelor-level 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, Levi-Civita 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 Friedman-Lemaitre-Robertson-Walker and Schwarzschild (although the latter will be redone in detail).  
Test information
Written exam (open book)
Specifics

Required materials
Reader
Klaas 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 materials
Book
Eric Poisson, A relativist's toolkit: The mathematics of black-hole mechanics
ISBN:9780521537803
Title: A relativist's toolkit: The mathematics of black-hole mechanics
Author:Eric Poisson
Publisher:Cambridge University Press
Edition:1
Costs:60.00
Instructional modes
Course

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

Tests
Tentamen
Test weight1
OpportunitiesBlock KW4, Block KW4

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