Daily Archives: August 31, 2008

Bit From Trit, and Lubos’ Booboo

Black holes and the standard model is a bit out of whack, as far as symmetry goes. I’ll discuss the issues, and then discuss how I think the problem is solved.

Quasinormal modes of vibration of black holes.
One of the curiousities of attempts to unify general relativity and the standard model is the quasinormal modes of vibration of black holes. This requires a little explanation.

It’s long been known that black holes exponentially approach a condition where the only numbers that characterize them is their mass, their spin, and their electric charge. This is sometimes called the “black holes have no hair” theorem, also known as Price’s Theorem, but named the “no hair theorem” by John Wheeler.

Suppose we begin with a black hole that has just a little hair, that is, we begin with a slightly perturbed black hole, one that is not quite symmetric. Over time, this hair will disappear. In the process of disappearing, the perturbation will change. As the perturbation dies out, it is possible that the perturbation will act as a sine wave multiplied by an exponential decay: \exp(-at) \;\sin(bt) , where a and b are constants with units of 1/time. If so, the constant b defines a characteristic frequency of this particular perturbation. And this is a fundamental characteristic of the black hole.
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