From: Hal Finney (hal@finney.org)
Date: Sat Dec 07 2002 - 06:41:59 MST
Mike Lorrey writes:
> 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?
So this would be a frictionless motor that we can feed energy into
indefinitely. As we do so the effective mass rises and it seems that
it should become a black hole.
I don't think this will work, for a couple of reasons. The Schwarzschild
radius for the entire Earth is only about half a centimeter. Assuming
your motor is at least that big, you must give it an effective mass at
least as much as the entire Earth, which is about 10^25 kg. So you will
need to boost your rest mass by about a factor of 10^25. I think it's
obvious that buckytube fibers, while strong enough for a space elevator,
won't withstand forces 25 orders of magnitude greater.
More fundamentally, gravitation is more than just effective mass.
Relativity adds a gravitational version of magnetism (that is, what
ordinary magnetism is to electric fields, gravitational magnetism is
to gravitational fields). When you achieve high effective masses via
relativistic velocities, the gravitational "magnetic" forces are just
as important as the static ones. In short, I don't think you will get
a black hole by spinning even an infinitely strong object, because it
is dynamically unstable and wants to explode. The outward forces are
always going to be greater than the inward ones. What you'll get is
some kind of spinning region of spacetime in the vicinity of the motor,
but you won't get gravitational collapse.
Hal
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