Re: Why must light rays always move parallel to each other at the event horizon

OK, fantastic question.  This is without a doubt the most advanced question
I've been given on the MadSci network.  But it's not so tough to see why
light would travel in only parallel lines at the event horizon, or at least
light that doesn't get sucked up by the black hole.  Assume a static black
hole (I'll get into this again in a minute), and consider light being
emitted by atoms falling into the black hole.  What light can escape from
just above the surface?  Only light that's moving straight away from the
black hole can.  From far enough away light can orbit the black hole in its
photon sphere, but from just outside the event horizon any deviation from
normal to the surface will result in a path for the photon that will take
it back into the black hole.  

Now take this one step further and consider what a black hole is.  What
causes the light to bend?  Space itself is stretched, this causes the bend.
 Light rays in empty space always travel in "straight" lines, but the path
that defines "straight" locally is determined by space itself.  If you
stretch space enough in one direction (towards the black hole), all paths
through space approach parallel to that direction.  Imagine space is a grid
of discrete points (some theories of the very small-scale structure of
space assume this), and think only in 2-D for simplicity.  Stretch space in
one direction (make the x-coordinate spacing larger as the y-coordinate,
for example), and your motion through space is defined in terms of a number
of points you move per unit time.  Travelling at a 45 degree angle (as an
example) means you move one point in x for every point in y.  Now make x
larger and y smaller again and you can see how you get closer and closer to
parallel to the direction of stretching.  The same thing is happening in 4D
near a black hole, space is being stretched in the direction of the
singularity.  The event horizon represents the distance at which the
stretching becomes infinite and all paths lead "straight" into the event
horizon.  So it's not only the light that's moving straight away that can
escape from just above the surface, it's that space itself is connected in
straight lines at the event horizon.  As an example of the infinite
stretching, time (dimension 4) stops, meaning that there's an infinite
distance between points in time as seen by an outside observer.  Of course,
more material being added to the black hole does increase its mass and
hence radius, therefore black holes can still absorb matter.  Hawking used
the fact that nearby light rays are parallel or moving away from each other
at the surface to prove that classical (non-radiating) black holes must
always increase in size.

On a side note, Hawking proved that black holes radiate.  Because the
radiation depends on the tidal force at the surface (larger for smaller
black holes), small black holes radiate faster.  So a real black hole is
not static, and this significantly complicates notions like time stopping
at the event horizon, since the event horizon can move as the black hole
absorbs matter and evaporates.  Therefore, all statements you read about
black holes should (eventually) be qualified by the specifics of the black
hole you're talking about.  But this is beyond the scope of your question.