American Association of Physics Teachers

 Don Marolf's TALK  -- p. 5
Teaching Black Holes

from the AAPT Topical Workshop:
Teaching General Relativity to Undergraduates
Syracuse University, July 20-21, 2006

Don Marolf

Click the link to see the full resolution PowerPoint slides for Marolf's talk. To see his extensive course notes that usefully supplement his talk download the PDF from

Pg. 1 Marolf's talk "Teaching Black Holes" described the one-semester course on SR, GR, and cosmology that he teaches to a class of 20-30 students with only calculus as a prerequisite.

He uses the 'physics first' approach, building his course around an exploration of the idea of the event horizon and its relation to the black hole.  He uses spacetime diagrams as a principal tool of analysis.

Pg. 2 To be useful they must be rescaled, i.e. set c = 1.  They can then be used to develop a representation of constant acceleration consistent with the ideas of relativity (PDF).  Due to the observer's motion, information in certain parts of the spacetime is inaccessible to the accelerating observer; the boundaries of these regions constitute horizons.

Examining the front and back ends of a very long rocket in an accelerated frame, he shows how to extract quantitative information from spacetime diagrams of accelerating frames. You can also do this kind of analysis with, for example, the Schwarzschild metric,

Pg. 3 but, Marolf strongly argues, spacetime diagrams are pedagogically more effective than mathematical formalism for introducing students to acceleration in SR and GR. He illustrated his point using 3-dimensional spacetime diagrams (t,x,y) to look at flat spacetime from different perspectives and to examine a simple star.

(He also reminded us that "drawing a picture always explains a lot to the person who draws the picture.")

Pg. 4 The star provides a way to show how as it compacts under gravity a horizon develops along with trapped rays of light.  The possibility of a black hole emerges.

Pg. 5 Make the star smaller while keeping the mass constant.  Diagrams show approach to Schwarzschild radius. They show a boundary between inside and outside regions with light rays unable to escape: a black hole.  All information which enters is trapped.

GR predicts black holes
Spacetime can become highly curved and a horizon forms
Light rays become trapped -- a black hole



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