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arXiv · 1804.09765

Sector models - A toolkit for teaching general relativity: III. Spacetime geodesics

Ute Kraus·Corvin Zahn
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Abstract

Sector models permit a model-based approach to the general theory of relativity. The approach has its focus on the geometric concepts and uses no more than elementary mathematics. This contribution shows how to construct the paths of light and free particles on a spacetime sector model. Radial paths close to a black hole are used by way of example. We outline two workshops on gravitational redshift and on vertical free fall, respectively, that we teach for undergraduate students. The contribution also describes a simplified calculation of the spacetime sector model that students can carry out on their own, if they are familiar with the Minkowski metric. The teaching materials presented in this paper are available online for teaching purposes at http://www.spacetimetravel.org . ----- Sektormodelle ermöglichen einen modellbasierten Zugang zur Allgemeinen Relativitätstheorie, der auf das Verständnis der geometrischen Konzepte abzielt und in seinen mathematischen Anforderungen nicht über Schulmathematik hinausgeht. Dieser Beitrag zeigt, wie die Bahnen von Licht und freien Teilchen auf einem raumzeitlichen Sektormodell konstruiert werden können. Als Beispiel dienen radiale Bahnen in der Nähe eines Schwarzen Lochs. Wir beschreiben zwei Workshops zu den Themen gravitative Rotverschiebung sowie radialer freier Fall, die wir in dieser Form mit Bachelorstudierenden durchführen. Der Beitrag beschreibt auch eine vereinfachte Berechnung des verwendeten raumzeitlichen Sektormodells, die von Teilnehmer/innen selbstständig durchgeführt werden kann, falls sie mit der Minkowskimetrik vertraut sind. Die vorgestellten Materialien stehen online unter http://www.tempolimit-lichtgeschwindigkeit.de für den Unterricht zur Verfügung.

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Ute Kraus, Corvin Zahn. 2018-04-25. Sector models - A toolkit for teaching general relativity: III. Spacetime geodesics. https://doi.org/10.1088/1361-6404%2Faae3b5

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