From: Anders Sandberg (asa@nada.kth.se)
Date: Sat Dec 07 2002 - 14:03:58 MST
On Sat, Dec 07, 2002 at 11:27:04AM -0800, Mike Lorrey wrote:
> THinking over an idea based on something I picked up off a KeelyNet
> list:
>
> Assume a superconducting motor, operating in a vacuum, fed as much
> power as it can handle indefinitely, bound by buckyfiber. At what point
> does it's velocity rise so high that it's mass/energy quotient causes
> it to implode into a black hole? Is this within the bounds of the
> strength of buckyfiber to hold it together to this point?
Exactly what is a superconducting motor? Your description sounds like
some kind of electrical device where electromagnetic fields are used to
accelerate the rotation of some part. In this case the answer is rather
clearly no: buckyfiber is far too weak to hold together macroscopic
objects rotating at relativistic speeds (it is limited by the strength
of molecular bonds), and you cannot make a black hole by increasing the
angular momentum density in a region of space - the angular momentum
causes frame dragging and other weird effects, but does not form a black
hole. It follows from the Kerr and Reissner-Nordström metric that you
can only get a black hole if a^2+e^2 < (GM/c^2)^2 where a is the
specific angular momentum (a=J/Mc), e is the specific charge and M is
the mass. Too much charge or momentum, no hole. Too bad.
There is also apparently a theorem somewhere (I think it also easily
follows from the third law of black hole thermodynamics) that says you
cannot break a black hole by spinning it up with external fields. A
pity.
> Note that the mass of such a black hole would be so small that it would
> rapidly evaporate (as predicted by Hawking) in a rather catastrophic
> explosion, converting its mass to energy.
It would be nice if we could pull this off. Some kind of compression
approach, putting energy into cavity modes that have a singularity at
the origin (such as the Bessel functions of the second kind)? Piling
bosons on top of each other?
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