Jan 25, 2012

Does the Kerr Solution Support the New “Anchored Rotating Reeb Foliation” of Fröhlich?

Posted by in categories: existential risks, particle physics

Roy Kerr found a beautiful solution to the Einstein equation 49 years ago. He long deserves a Nobel Prize. The recent Telemach theorem (in print in the African Journal of Mathematics) modifies the appearance of every solution “close” to a black hole’s horizon.

What Dieter Fröhlich discovered in yesterday’s chaos course at the University of Tübingen started out from the fact that every rotating black hole has a nonrotating horizon owing to the infinite local slowdown of time. We had concluded before that the in-spiraling trajectories must form something like a “Reeb foliation” on the way to the unmoving horizon. He suddenly realized that an “anchored rotating Reeb foliation” is the answer.

I repeat: We had conjectured before that In between the outer unstable limit cycle of in-spiraling trajectories and the inner motionless horizon, there exists a “circular chain of cups” – non-crossing trajectories that in a U-turn-like fashion connect the two limiting trajectories (the unstable outer limit cycle and the stable inner limit cycle of opposite orientation). Such a beautiful differential-topological flow was discovered in 1952 by Georges Reeb (as had been pointed out to me by Art Winfree).

However, the problem is that the attractive inner limit cycle has rotation rate zero. Does this not destroy all hope for consistency? Fröhlich saw the solution in a flash: Put the standard Reeb foliation into a rapidly spinning motion, which makes no qualitative difference. Then smoothly reduce the cups’ rotation rate until the attractive inner limit cycle becomes a singular spiky (“star-node related”) limit cycle while the ring of “cups within cups” retains a constant rotation rate. The obtained “anchored rotating Reeb foliation” (anchored everywhere on the horizon) represents a new differential-topological prototype, embraced by nature.

It would be marvelous to get a response from Professor Kerr himself. (For J.O.R.)

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