Sector Models - A Toolkit for Teaching General Relativity. Part 1: Curved Spaces and Spacetimes

TL;DR

This paper introduces sector models as an accessible, conceptual teaching tool for general relativity, enabling students to understand curved spaces and spacetimes without advanced mathematics.

Contribution

It presents a novel approach using sector models to teach curved spaces and spacetimes in an intuitive way suitable for high school and undergraduate students.

Findings

Sector models effectively illustrate curved spaces and black holes.

Workshop activities enhance understanding of general relativity concepts.

Models are suitable for online and classroom teaching environments.

Abstract

Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary mathematics. The central idea of this introduction to general relativity is the use of so-called sector models. Sector models describe curved spaces the Regge calculus way by subdivision into blocks with euclidean geometry. This procedure is similar to the approximation of a curved surface by flat triangles. We outline a workshop for high school and undergraduate students that introduces the notion of curved space by means of sector models of black holes. We further describe the extension to sector models of curved spacetimes. The spacetime models are suitable for learners with a basic knowledge of special relativity. For online teaching materials, see http://www.spacetimetravel.org . ----- F\"ur die Vermittlung der Allgemeinen Relativit\"atstheorie in der Schule, im Grund- oder im Nebenfachstudium besteht das Anliegen, eine fachlich befriedigende Darstellung zu geben, die nicht mehr als Schulmathematik voraussetzt. Wir stellen in diesem Beitrag einen solchen Zugang vor. Das zentrale Werkzeug unserer Einf\"uhrung sind sogenannte Sektormodelle, die gekr\"ummte R\"aume im Sinne des Regge-Kalk\"uls durch eine Zerlegung in kleine, ungekr\"ummte Sektoren beschreiben, \"ahnlich der Triangulierung einer gekr\"ummten Fl\"ache. Wir schildern einen Workshop f\"ur Sch\"uler/innen und Studierende, in dem gekr\"ummte R\"aume anhand von Sektormodellen Schwarzer L\"ocher eingef\"uhrt werden. Wir beschreiben ferner die Erweiterung auf Sektormodelle gekr\"ummter Raumzeiten. Raumzeitliche Sektormodelle setzen Grundkenntnisse der Speziellen Relativit\"atstheorie voraus. Online-Materialien unter http://www.tempolimit-lichtgeschwindigkeit.de .