This website, www.GaugeGravity.com is about the theory of gravity found by the Cambridge geometry group.

The beauty of this theory is that it provides predictions that are identical to the usual general relativity, but it is considerably simpler.

The first simplification is that it can be made to use a flat spacetime. This means that objects like black holes can be easily analyzed. If you want to see physicists get angry, bring up the subject of changes to Einstein's general relativity. Lubos Motl wrote a post arguing against variable speed of light (VSL) theories. Or course any flat space gravitation theory has to use a variable speed of light. While Gauge Gravity is not usually described as a "VSL" theory, I've nevertheless written a rebuttal to Motl's post here.

When one models a black hole in gauge gravity, one uses Painleve coordinates. I've written up a Java applet gravity simulator that uses both Schwarzschild and Painleve coordinates. To transform between Schwarzschild and Painleve coordinates, one leaves all the coordinates of an event unchanged except time. One adds or subtracts a constant that depends on the radius. So Painleve coordinates are quite similar to Schwarzschild. The most obvious difference is that in Schwarzschild coordinates, a particle that falls into a black hole gets stuck on an event horizon. In Painleve coordinates, they continue on to the origin.

Gauge gravity uses geometric calculus instead of tensors. Geometric algebra is an application of Clifford algebra to a manifold. In short, you associate the canonical basis vectors of the Clifford algebra with the tangent vectors of the Geometric algebra, and choose the signatures for the canonical basis vectors to match the natural signature of the spacetime you want.

Now with this definition, you automatically end up with an algebraic structure for the geometric algebra that (at each point in spacetime) is equivalent to square matrices (more or less). You can then break these up into the tensors by picking out symmetry elements of the square matrices.

For example, one could take the component of a square matrix that lie on the diagonal, average them, and one would get the component of the square matrix that corresponds to a scalar. This you would map to the scalar tensor. But in doing this, one finds that it is far more elegant to leave the tensors together in geometric form.

This website is very young. If there are things you want added, put a comment in the guest book, or add on to the wiki. I'll get around to adding a lot more later, but it will be some time as I have a bunch of other websites I've just started and will get back to this one later.

That reminds me. If you want the job of maintaining this website contact me by email at carl at brannenworks dot com. It's a wonderful job with only one bad part, the pay (which is zero). On the other hand, you're not expected to make a profit (the website has no income), and the likelihood that you will keep your job is quite high. So if this is your subject, and you want to learn it by researching it and teaching it, this will be something you will find very useful.

Carl Brannen

This is one of several educational websites that I've recently started, to see more about them, click the "about" button. Of particular interest with respect to the present subject is
http://CliffordAlgebra.com