starship-design: Black holes: a mystery

[Steve VanDevender <stevev@efn.org>]

kyle writes:
 > So what happens when you're just outside of a black hole's event
 > horizon?  Something is pulling you toward the black hole, very
 > powerfully, but what?  If gravitons are emerging from the black hole
 > to pull you in, then they must be travelling faster than light; not
 > even light can escape a black hole.  So how can gravitons escape??

It's a common misconception that what prevents you from escaping from a
black hole is an escape velocity faster than light.  Unfortunately this
is both relativistically meaningless and not borne out by a more careful
analysis of how black holes work.  Just the finite radius and mass of a
black hole will tell you that its escape velocity is less than c, even
taking general relativistic effects into account.  When I was about
your age, Kyle, I used purely classical means to derive an expression
for black hole radius-vs.-mass that I later learned was off by a factor
of two because I didn't know general relativity.  Such are the perils of
being a young physics student.  My analysis was based on escape
_energy_; if it takes more energy than a particle contains for it to
escape, then it cannot.

What really makes a black hole inescapable is that once you pack enough
mass within a critical radius the spacetime curvature within that radius
become degenerate.  All movement in space or time leads inexorably
towards the central singularity; you can't escape and you can't even
stand still.  I don't think that even moving faster than light would
help; you'd just get to the singularity faster.

Black hole evaporation is the result of virtual particle creation, but
the virtual particles escape not because they travel faster than
light, but because they are created just above the event horizon, and
hence are capable of escaping if they have enough energy.  Black holes
evaporate at a rate dependent on their mass, where much more massive
black holes with less extreme gravity gradients evaporate at an almost
imperceptible rate and small black holes evaporate rapidly, even
explosively at the end.  Quantum black holes, unless they were
continually supplied with mass, all would have evaporated by now, and
forming new ones is difficult because the high rate of evaporation makes
it difficult to pump enough mass into them to keep them from evaporating
away.

Furthermore, gravitons are pretty speculative at this point; although
quantum mechanics and general relativity are both successful,
well-tested theories they have not been combined into a well-accepted
unified theory.  Einstein tried for much of his career but his inability
to accept certain aspects of quantum mechanics probably kept him from
succeeding.

We do know that there are concentrations of mass in the universe that
appear to be black holes, both from their characteristic radiation and
the movement of mass in their vicinity.