Studying null and time-like geodesics in the classroom

Thomas Müller (1), Jörg Frauendiener (2)

In a first course of general relativity it is usually quite difficult for students to grasp the concept of a geodesic. It is supposed to be straight (auto-parallel) and yet it 'looks' curved. In these situations it is very useful to have some explicit examples available which show the different behaviour of geodesics. In this paper we present the GeodesicViewer, an interactive tool for studying the behaviour of geodesics in many different space-times. The geodesics can be represented in several ways, depending on the space-time in question. The use of a local reference frame and 'Cartesian-like' coordinates helps the students to develop some intuition in various situations. We present the various features of the GeodesicViewer in the form of readily formulated exercises for the students.

The Geodesic Viewer
The most recent version of the GeodesicViewer can be downloaded here:

Linux source files gzip-compressed tar-file (3.0MB) md5: d051902f42f4be3b3472ef75329b0f28
Windows source files zip-archive (3.3MB) md5: fea3fe50f8738ffbb1d018929206d682
Windows binaries zip-archive (17MB) md5: 21d77f1d0ea99b379ea60509d37bf8f9
exercise files zip-archive (503kB) md5: e826c59c641dd00fb72a3c9546ec79db

Version date: 25. Mar 2011 

A brief documentation, some tutorials, and an installation instruction can be found here.
Note that the Windows binaries were tested only on 64bit 'Windows 7/XP' machines.

Screenshots of Exercises
The configuration files can be found in the 'exercise files' zip-archive.



(1) Visualisierungsinstitut der Universität Stuttgart (VISUS)
Allmandring 19
70569 Stuttgart, Germany

(2) Department of Mathematics & Statistics, University of Otago,
P.O. Box 56, Dunedin 9010, New Zealand