General Relativity Autumn 2021

Corona Info, Lecture Notes, Exercises, Solutions, and more ...

The most recent and up-do-date information about this course will always be available here!

The Course and Lectures: How and When and Where

At the moment, the plan is to hold the GR Course in-person (als Präsenzveranstaltung).
There is no need to register for this course, but if you are going to take part please send me an email (blau at itp unibe ch) so that I can set up a mailing list. Thank You!
Note: the latest (September 14) rules are that a COVID Certificate is required to attend the course (and wearing masks also remains compulsory)! Webpage with further information
Moreover, please watch the UniBe Corona and Teaching Webpage and the linked Websites (FAQs) and files for updated information.
The schedule is:
- Monday 13h15 -- 15h
- Tuesday 12h15 -- 14h
The course will take place in Lecture Hall 119 and we will start on Monday September 20 at 13h15
Exams: Oral exams will take place in the week 14.-18. February 2022. Further information will be given below. In accordance with the latest rules issued by the university, all exams will take place online via Zoom.
Further Information: Please watch this page for the latest information about the course and the lectures! (e.g. a switch to an online zoom format etc.)

Lecture Notes

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

Prerequisites

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
- ...

Exercises and Solutions

Oral Exams

Dates:
- The oral exams will take place in the week 14-18 February 2022.
  This period should be regarded as compulsory for all Theory Master Students, unless
  - either you are unable to take the exam during that week due to Military Service
  - or you already have two or more exams scheduled for that week (proof required).
  In that case, please contact me for individual apppointments.
- Please sign up for the exam via KSL.
  Note: exam date and time given in KSL are of course fictitious. See the information below for available slots and contact me for preferred time *after* you have registered for the exam in KSL.
  (Individual appointments will also be added to the list below.)
Available/Confirmed Dates and Time:
- February 14, 11h:
- February 14, 12h: Moritz Meyer zu Westram
- February 14, 14h: Immanuel Albrecht
- February 14, 15h:
- February 15, 11h: Daniil Krichevskiy
- February 15, 12h: Marc Schneiter
- February 15, 14h: Peter Krack
- February 15, 15h: Andrin Sprecher
- February 17, 11h: Lukas Born
- February 17, 12h: Julian Meier
- February 17, 14h: Sergio Andres Joya
- February 17, 15h: Julian Eicher
- Other Date/Time:
- January 12, 10h: Jan Herrmann
- January 12, 11h: Valentin Wyss
- February 25, 11h: Michele Wyss

Further Information:
- In accordance with the latest rules issued by the university, all exams will take place online via Zoom.
- For Zoom exams a Tablet/iPad or something equivalent is required.
- Zoom Question (and Answer!) Session:
  - date changed to Tuesday February 8, 13:15

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
I also expect you to be thoroughly familiar with the Exercises!

2020 Nobel Prize in Physics

Information from the Nobel Prize Website:

John Baez' characteristically lucid explanation of Roger Penrose's work:

Roger Penrose's Nobel Prize (by John Baez)

Highly Recommended Literature

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

GR Lectures Notes on the WWW and related Online Resources

Note: the resources mentioned below are approved/recommended. If you come across, and want to use, some other online resources, please come and show them to me (also in GR, there is much more low- than high-quality stuff floating around on the WWW and it may not always be easy for you to decide at first sight which is which).
Please let me know of any broken (no longer existing) links.