Studying null and time-like geodesics in the classroom

TL;DR

This paper introduces the GeodesicViewer, an interactive educational tool designed to help students visualize and understand null and time-like geodesics in various space-times, enhancing intuition in general relativity courses.

Contribution

It presents a novel interactive software that provides explicit examples and visualizations of geodesics, aiding teaching and learning in general relativity.

Findings

The tool effectively illustrates geodesic behavior in different space-times.

Students can develop better intuition through visualizations and exercises.

The software supports multiple representations and coordinate systems.

Abstract

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.