- Monday 13h15 -- 15h, Tuesday 12h15 -- 14h, room 119
- Starting Date: Monday September 16th

- GR Lecture Notes Website (overview)
- [newlecturesGR.pdf] (direct link to the pdf-file)
- Note: this new version has 900+ pages (!). Please save trees and don't print all of it at once, we will only cover some small parts of the notes in the course

- Covariant Formulation of Special Relativity (Minkowski Geometry, Lorentz Tensor Algebra etc.)
- Classical Field Theory (Action Principles for Fields)
- Multivariable Calculus

- Physical and Mathematical Foundations of General Relativity
- Equivalence Principle
- Geodesics
- Tensor Algebra and Tensor Calculus
- Riemannian Geometry and Curvature Tensor
- Physics in a Gravitational Field
- Einstein-Equations and Einstein-Hilbert Action

- Selected Applications
- Solar System Tests of General Relativity
- Black Holes
- Basics of Cosmology
- ...

- Assignments 01
- Solutions 01
- Optional Assignment + Solution 02
- Assignments 03
- Solutions 03
- Assignments 04
- Solutions 04
- Assignments 05
- Solutions 05
- Assignments 06
- Solutions 06

- KSL:
If you are planning to take the exam in January / February 2019, please sign up for the exam via KSL until latest January 30th!

(If you are planning to take the exam at a much later stage, there is no need to sign up now.) - Dates:
- Theory Master Students: February 04/05/06. See the information below for available slots and contact me for preferred time.
- Others: If you are happy with these dates, please also
sign up for one of these slots. If not,
contact me for individual appointments.

(These appointments will then also appear in the list below.)

- Confirmed/agreed Dates and Time:
- February 04, 11h: Igor Jurosevic
- February 04, 12h:
- February 04, 14h: Rafael Moser
- February 04, 15h:
- February 05, 11h: Barbara Jenny
- February 05, 12h:
- February 05, 14h: Antea Doriot
- February 05, 15h:
- February 06, 11h: Tabea Krucker
- February 06, 12h: Linus Vogt
- February 06, 14h: Merlin Utiger
- February 06, 15h:
~~Omar Celikbas~~ - February 21, 11h: Caroline Haslebacher
- February 21, 12h: Omar Celikbas
- February 24, 14h:
~~Anja Gauch~~(postponed to March) - February 24, 15h:
~~Jo Ann Egger~~(postponed to March)

- Further Information:
- Exams take place in my office (220a).
- Upon request, we can organise a Question (and Answer!) Session some time in January. Let me know.
- Feel free to come to my office (with or without prior appointment) if you have any questions.
- However: I will not answer questions via e-mail - my experience is that this is likely to lead to more confusion than understanding.

- Contents: During each exam, I will try to touch upon the following 4 general
subjects:
- Dynamics of Particles and Fields in a Gravitational Field:

metric and gravitational field, geodesic equation, action principle, Newtonian limit, redshift, conserved charges, minimal coupling, scalar field, definition of energy momentum tensor etc - Dynamics of the Gravitational Field:

Einstein equations and their main properties (definition of Riemann, Ricci etc, number of equations, role of Bianchi, ...). Einstein-Hilbert action. vacuum Einstein equations etc - Schwarzschild Metric and the Solar System:

main properties of the metric; derivation of the effective potential and orbit equations; main qualitative difference(s) between Kepler and GR orbits etc - Schwarzschild Metric and Black Holes:

significance of r=2m: what happens or does not happen there; tortoise and Eddington-Finkelstein coordinates; freely falling versus static observers; behaviour of lightcones; Kruskal diagram etc

- Dynamics of Particles and Fields in a Gravitational Field:

- Lemaitre Symposium at UniBe 21.11.19
- V. Mukhanov (LMU Munich): How predictive are cosmological theories? Wednesday, 27.11.2019, 16:15, ExWi B6
- In the Spring Semester (FS20), I will give a Master/Graduate
Course on Selected Advanced Topics in General Relativity (more on Black Holes
and other fun things):
- Preliminary Schedule: Weeks 1-7 of the Semester, Thursday 14-17h
- Preliminary List of Topics:
- Review of the Schwarzschild Black Hole
- Guided Visit to the Zoo of Black Hole Solutions
- Classical Theory of Black Holes
- Carter-Penrose Conformal Diagrams
- Unruh Effect, Hawking Temperature and Hawking Radiation
- Aspects of Black Hole Entropy and Black Hole Thermodynamics
- Outlook/Wild Stuff: Information Paradox / Firewalls / AdS/CFT / Black Holes and Quantum Information Theory etc

- Information for Theory Master Students:
- Please regard this course as an optional additional course. The main Specialist Course offered by the ITP this semester is the course Conformal Field Theory by Susanne Reffert, which you are strongly encouraged to attend.
- In order to compensate the reduced number of hours compared to a regular Specialist Course, to acquire the ECTS for this course you will need to do a homework project / presentation based on the contents of the course. Details to be discussed at a later stage.

- Excellent Introductory (Undergraduate) Text
- J.B. Hartle: Gravity, An introduction to Einstein's General Relativity
- Elegant Modern Slightly More Advanced Books
- R.M. Wald: General Relativity
- S. Carroll: Spacetime and Geometry, an Introduction to General Relativity
- Classics
- C.W. Misner, K.S. Thorne, J.A. Wheeler: Gravitation
- S. Weinberg: Gravitation and Cosmology
- Other Personal Favourites
- R.U. Sexl, H.K. Urbantke: Gravitation und Kosmologie
- N. Straumann: General Relativity
- S.W. Hawking, G.F.R. Ellis: The Large Scale Structure of Space-Time
- E. Poisson: A Relativist's Toolkit
- Other Recommended Recent/New Books
- A. Zee: Einstein Gravity in a Nutshell

Please let me know of any broken (no longer existing) links.

- Albert Einstein: Die Grundlage der allgemeinen Relativitätstheorie (Annalen der Physik, 1916)
- Einstein Papers Project
- Einstein Papers Project (The Collected Papers of Einstein)
- Digital Einstein Papers (including English translations)
- Schriften 1914-1917 (in German)
- Writings 1914-1917 (in English)
- The Field Equations of Gravitation (November 25 1015)
- etc etc (thank you to everyone involved in this project!)
- GR Lecture Notes: General
- Harvey Reall: General Relativity (Univ. of Cambridge Lecture Notes)
- Piotr Chrusciel: General Relativity I and II
- Don Marolf: Notes on Relativity and Cosmology
- Gerard 't Hooft: Introduction to General Relativity
- Gary Gibbons: General Relativity
- Sean Carroll: Lecture Notes on General Relativity [see also the links at the bottom of that page]
- Philippe Jetzer: General Relativity
- GR Lecture Notes: Black Holes
- Gerard 't Hooft: Introduction to the Theory of Black Holes
- Paul Townsend: Black Holes
- J.P. Luminet: Black Holes : A General Introduction
- For observational and astrophysical evidence for black holes see
- S.A. Hughes: Trust but verify: The case for astrophysical black holes
- A. Mueller: Experimental Evidence of Black Holes
- C. Bambi: Astrophysical Black Holes: A Compact Pedagogical Review
- For more mathematical discssuions see
- P. Chrusciel: The Geometry of Black Holes (includes discussion of advanced topics in mathematical GR)
- D. Christodoulou: The Formation of Black Holes in General Relativity (594(!) pages, mathematical general relativity, not for the faint of heart)
- GR Lecture Notes: Cosmology
- Was Einstein Right? (Ask Clifford M. Will!)
- Clifford M. Will: The Confrontation between General Relativity and Experiment (arXiv version)
- Clifford M. Will: Was Einstein Right? A Centenary Assessment (abridged version of the article above)
- Clifford M. Will: The 1919 measurement of the deflection of light
- GR Lecture Notes: Other
- Living Reviews in Relativity (high quality review articles on all aspects of relativity -recommended!)
- Ingemar Bengtsson: Anti-de Sitter Space
- List of Online GR Books and Lecture Notes (no warranty)
- Other Useful, Informative or Entertaining Online Resources
- Wikipedia: Equivalence Principle
- R. Wald: Teaching General Relativity
- Sean Carroll's No-Nonsense Introduction to General Relativity
- APS Journals: GR Centennial
- John Baez: the General Relativity Tutorial
- C. Lineweaver, T. Davis: Misconceptions about the Big Bang (highly recommended Scientific American Article)
- Visualisierung in der Relativitätstheorie (Uni Stuttgart), Studying null and time-like geodesics in the classroom
- Usenet Physics FAQ
- Einstein for Everyone (J.D. Norton)
- Einstein Archives Online
- RelativityBook.com Resources
- Picturing Black Holes (a nice introduction to Penrose diagrams, by J.D. Norton)
- A Peek into Einstein's Zurich Notebook( J.D. Norton)
- Einstein's `Zürich Notebook' and his Journey to General Relativity (N. Straumann, arXiv:1106.0900)
- Other Einstein Goodies (J.D. Norton)
- Terence Tao: The Cosmic Distance Ladder (pdf-file)
- Terence Tao: The Cosmic Distance Ladder (video of public lecture on youtube)
- Visualisation of Parallel Transport on the 2-Sphere (java applet)
- Gerard 't Hooft: Strange Misconceptions of General Relativity
- Wie man die Raumzeit krümmt
- Is our Universe a Black Hole?
**NO**And since I get asked this question again and again (as if there weren't more interesting questions), usually by people who understand neither cosmology nor black holes, here are some links: - Answer from the Physics FAQ: Is the Big Bang a Black Hole?
- Answer from Cosmic Variance
- Answer from Lubos Motl
- And another one
- arXiv:1001.4795: Through the Looking Glass:
Why the
Cosmic Horizon is not a horizon (a more detailed and technical account) - Important Advice (from Nobel Laureate Gerard 't Hooft):

- Matthias Blau, Office 220a