## page was renamed from Education Research on General Relativity/TestSpacetime
= Hildesheim University, Germany: Spacetime-Travel =

== Goals ==
  * '''Relativistic visualization.''' We develop visualizations of relativistic scenes from a first-person point of view using the ray-tracing method of computer graphics.
  * '''An introduction to general relativity using no more than elementary mathematics.''' We develop ways of teaching general relativity in school and in undergraduate physics. The focus is on grade 10 (age 16 years) and on university programs for pre-service physics teachers.

== Main activities ==
 * Creation of both interactive and non-interactive visualizations. Examples: Fall into a black hole, interactive flight simulator with relativistic speeds.
 * Creation of sector models. We have developed sector models as a novel way of representing curved spaces and curved spacetimes in a way that is coordinate-free and therefore amenable to geometric intuition. New sector models are created to visualize the properties of specific spacetimes.
 * Design of teaching units using sector models as tools. These units present theoretical concepts of general relativity (in particular geodesics and curvature) in a way that provides geometric insight. They require no more than elementary mathematics.
 * Tests of teaching units in school and at university.
 * Empirical studies: students' concepts on geometry, learning outcomes of model-based learning.

== Results ==
 * Teaching resources and research results are made available online at [[https://www.spacetimetravel.org]]. (German version [[https://www.tempolimit-lichtgeschwindigkeit.de]])

== Selected references ==
=== Sector Models ===
 * [[https://iopscience.iop.org/article/10.1088/0143-0807/35/5/055020|C Zahn and U Kraus, Sector models—a toolkit for teaching general relativity: I. Curved spaces and spacetimes, 2014 Eur. J. Phys. 35 055020]], open access: [[https://www.spacetimetravel.org/sectormodels1/sectormodels1.html]]
 * [[https://iopscience.iop.org/article/10.1088/1361-6404/aae3b7|C Zahn and U Kraus, Sector models—a toolkit for teaching general relativity: II. Geodesics, 2019 Eur. J. Phys. 40 015601]], open access: [[https://www.spacetimetravel.org/sectormodels2/sectormodels2.html]]
 * [[https://iopscience.iop.org/article/10.1088/1361-6404/aae3b5|U Kraus and C Zahn, Sector models—a toolkit for teaching general relativity: III. Spacetime geodesics, 2019 Eur. J. Phys. 40 015602]], open access: [[https://www.spacetimetravel.org/sectormodels3/sectormodels3.html]]

=== Visualization ===
 * [[https://iopscience.iop.org/article/10.1088/0143-0807/29/1/001|U Kraus, First-person visualizations of the special and general theory of relativity, 2008 Eur. J. Phys. 29 1]], open access: [[https://www.spacetimetravel.org/ejpvis/ejpvis.html]]