organized by the University of Potsdam and the Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
4th – 15th March 2013
The University of Potsdam and the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) offer a crash course on the physical and mathematical foundations of gravity. This course can be attended by students studying in their 5th semester Physics or Mathematics. The seminar consists of two separate lecture series (to be held in English):
- Introduction to General Relativity (Jeremie Joudioux, Martin Reiris)
- Mass and energy of isolated gravitating systems (Gerhard Huisken)
- Cosmology (Lars Andersson, Alexander Wiegand)
The timetable is arranged to provide two lectures in the morning, each one lasting 90 minutes. In the afternoon there will be opportunities for questions and discussions.
The lectures will take place daily from 9.00-10.30 and 11.00-12.30 in the lecture hall of the main building of the Max Planck campus in Golm (near Potsdam).
Participants studying outside the area Potsdam-Berlin will be supported financially with 200 Euros. The `Fachschaft Physik’ of the Universiy of Potsdam will provide assistance in finding accomodation. Information on how to get to the Max Planck campus in Golm can be found here.
Contact Person
Prof. Lars Andersson
Max Planck Insitute of Gravitational Physics
Am Mühlenberg 1
14467 Potsdam-Golm
e-mail:
Registration
Registration has been closed!
Abstracts
Introduction to General Relativity (Jeremie Joudioux, Martin Reiris)
We start the introduction of the physical fundaments of General Relativity (GR) by reviewing the concepts of time, space, mass and force in Newtonian physics as well as in Special Relativity. We then present the basic assumptions of GR, i.e. the Lorentzian spacetime structures and Einstein’s field equations, and discuss some empirical tests of GR. Further topics in the course include the initial value problem, spherically symmetric spacetimes, gravitational radiation, star models, gravitational collapse, and black holes.
Mass and energy of isolated gravitating systems (Gerhard Huisken)
The lectures investigate Lorentzian 4-manfolds modelling isolated gravitating systems such as stars and black holes in the context of the Einstein field equations. It is a major aim in Mathematical Relativity to identify geometric structures that model classical physical concepts such as “mass”, “center of mass”, “momentum” and angular momentum in a natural way. We show how to use geometric variational principles to define “mass” and “center of mass” with the help of suitable hypersurface foliations in Lorentzian manifolds.
Cosmology (Lars Andersson, Alexander Wiegand)
This course will give an introduction to the basic principles of cosmology and an overview of cosmological models, including the Friedman models which play a central role in the standard model of cosmology. We will present current observational data and discuss their implications for models of our universe.
Requirements
Basic knowledge of differential geometry, Newtonian mechanics and gravity, special relativity. The notes skriptdiffgeo (on differential geometry) and skriptmechgrav (on mechanics and gravitation) will give some of the appropriate background material.
References
Introduction to General Relativity
- N. Straumann, General Relativity, Springer, Berlin 2004
- W. Rindler, Introduction to Special Relativity, Oxford University Press 1982
- N.M.J. Woodhouse, Special Relativity, Springer, Berlin 1992
- R. Wald, Space, Time and Gravity, University of Chicago Press, 1992
- C. Misner, K. Thorn, J. Wheeler, Gravitation, Freemann and Company, 1973
- H. Stephani, General Relativity, C.U.P.,1990
- S. W. Hawking, G. F. R. Ellis, The Large Scale Structure of Space-Time, C.U.P., 1975.
Mass and energy of isolated gravitating systems
- C. Cederbaum, The Newtonian Limit of Geometrostatics (Dissertation)
Cosmology
- Cosmology, Steven Weinberg, Oxford University Press, 2008.
- Observational cosmology, Stephen Sergeant,Cambridge University Press, 2010.
- Relativistic Cosmology, George F.R. Ellis, Cambridge University Press, 2012.
- The primordial density perturbation: cosmology, inflation and the origin of structure, David H. Lyth , Andrew R. Liddl Cambridge University Press, 2009
- Cosmic Microwave Background Anisotropies, Wayne Hu, Scott Dodelson
Course material
- Kerr example: PDF / notebook file
- Riemann: PDF / notebook file
- Maple worksheet and data file, related to the Cosmology lectures