Sunday, May 30, 2010

Deriving the Simplest Geometry - Greg Egan

n Chapter 12 of Incandescence, the Splinterites succeed in deriving a possible geometry for the spacetime they inhabit. They come up with the simplest possible geometry that conforms to Zak's principle (that the sum of the three perpendicular “weights”, or tidal accelerations, is zero, after the effects of spin have been removed) while explaining the fact that the ratio of the garm-sard weight to the shomal-junub weight is less than the apparent historical value of three.

The spacetime geometry that they discover is what we would call the Schwarzschild spacetime, which is the geometry of the vacuum around any spherically symmetrical body whose spin and electrical charge are zero, such as a non-rotating black hole. In the novel there is a rough sketch of how they performed their calculations; this page gives the details. Nothing here will require prior knowledge of general relativity, and anyone should be able to get the gist of it, but you'll need a bit of high-school level algebra, trigonometry and calculus if you want to verify every calculation along the way."

5 out of 5

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