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 workshop on redshift does not require knowledge of special relativity, the workshop on particles in free fall presumes familiarity with the Lorentz transformation. 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.
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Sector models - A toolkit for teaching general relativity: III. Spacetime geodesics
The teaching materials presented in the article can be used freely in class and can be downloaded here:
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