# That Black-Hole Space-time curvature thing

John K Clark (johnkc@well.com)
Thu, 11 Sep 1997 20:57:09 -0700 (PDT)

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On Thu, 11 Sep 1997 Sarah Marr <sarah.marr@dial.pipex.com> Wrote:

>Ok, so what I've never quite understood is this: why does the
>extreme curvature of space-time at the event horizon of a small
>black whole tear the intrepid astronaut to bits?

If no force is acting on the astronaut except gravity, that is, if he's
freely falling, then ever particle in the poor man is moving in parallel
straight lines, or rather the analog of parallel straight lines when you're
dealing with curved surfaces, a geodesic. 4 dimensional spacetime can be
thought of as the surface of a 5 dimensional sphere, but that can't really be
visualized so consider the 2 dimensional surface of a 3 dimensional sphere,
like the earth.

If I'm on the equator and want to go to the north pole by the shortest route
then there is only one path I can follow, a geodesic. Suppose I have company
on my trip because my neighbor, also on the equator 10 miles west of me,
is going to the pole by the shortest route too. Both out paths are absolutely
perpendicular to the equator and at first, when we've only gone a short
distance, my path and that of my neighbor seem absolutely parallel too, but
as we continue our journey we start to get closer together until at the pole
we collide. There was no force pushing us together, it's just what happens
when 2 people follow a geodesic on a sphere. Even if we were 2 dimensional
creatures incapable of visualizing the third dimension we could still deduce
that the ground must be curved in that mysterious direction because we find
that parallel straight lines converge if they're long enough, if fact that's
what is mente by a surface being curved.

At fist our astronaut feels no force as he falls into the central point of
the black hole, the singularity, because all his parts are moving straight
and parallel, and if space was flat things would stay that way, but it's
curved and the curve is increasing. Despite moving in parallel his parts are
nevertheless getting closes together and will continue to do so until every
particle in his body occupies exactly the same point in spacetime, he'd be
crushed to death long before that of course.

>When space-time distorts, as I understand it, 'new' space-time is
>not created, existing space-time merely stretches. But it stretches
>only in the context of an external point of view. Anything within
>that space-time would not see the stretching

If our astronaut was the size of a mathematical point then he would feel no
force and have no problem, but he's so big that his head and feet are in
VERY different reference frames, and that's not healthy for our poor friend.

John K Clark johnkc@well.com

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