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carlbrannen Says:

May 18th, 2007 at 6:53 pm

Okay, I’ve now visited the referenced website. The problem is that it has no numbers. But there is something to be said for the philosophy.

I took GR a very long time ago at U. Cal., Irvine. Ever since then I’ve wanted to write a GR textbook for undergraduates. That is, one that would concentrate on calculations that can be done without tensors, the “complex and cabalistic notation”.

For example, Misner Thorne and Wheeler doesn’t discuss orbits in the Schwarzschild metric until most of a thousand pages in. But the orbits can be found by applying calculus of variations to the integral of the line element ds, as the paths of test particles extremize proper time.

This is all undergraduate mathematics and requires no tensors. It does, however, get kind of messy, and it is possible to get a half decent education in GR without ever seeing the equations of motion written this way. This is the basis for the java applet simulation I wrote here.

The line elements that define a Schwarzschild (or Kerr) black hole can be shown to be solutions to the “no source” GR problem outside of their singularities. Thus these solutions can be found without the complex and cabalisitic notation.

carlbrannen Says:

May 18th, 2007 at 6:55 pm

Ooops. wordpress ate what I was trying to quote. At the beginning of my post a moment ago should be:

“Are calculations in General Relativity difficult? No. What is complex is the notation. Do you understand this? You need to eliminate the complex and cabalistic notation of General Relativity in order to make simple calculations. Calculations are not complicated, it is the notation which is complicated. And the notation obstructs easy calculations.”