Re: A partial black hole?

James Burns wrote:

> It says on the Wikipedia page that something falling
> into an event horizon will appear to redden and slow,
> never quite reaching the event horizon, because of
> the gravitational red****ft becoming infinite at
> the horizon.
> 
>
http://en.wikipedia.org/wiki/Black_hole#Before_the_falling_object_crosses_the_event_horizon


What they're referring to is what external observers _see_.  That's not 
the same thing as what actually happens to infalling observers.

You're far better off with a more reputable resource.  Take, for 
instance, the excellent sci.physics FAQ entry on this question:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

Think of it this way:  What external observers see is not the object 
falling, but the light it emits/reflects on its way down.  It should be 
easy to see that regardless of what infalling observers experience 
themselves, you will see this dimming and red****fting effect.

Take external observers far enough from the black hole that they are not 
directly experiencing relativistic effects (in practice this isn't too 
hard; a dozen or more Schwarzschild radii will suffice).  They watch as 
an object continuously emitting a laser beam falls radially in to a 
Schwarzschild black hole (we'll assume that the object is sturdy enough 
to survive intact and continue emitting its laser as it reaches the 
event horizon).  (If the light were reflected, it would only change what 
they see quantitatively because of the required round trip, not 
qualitatively, so let's deal with the simpler case.)

What do they see?  Well, at first, they don't see anything unusual; the 
laser beam looks normal.  As the emitter approaches the event horizon, 
however, relativistic effects start to dominate.  First, the photons of 
the laser are progressively more red****fted due to gravitational 
red****ft.  However, it takes progressively longer and longer for photons 
emitted from nearer and nearer to the horizon to escape to distant 
observers due to gravitational time dilation, as well.  This is viewed 
as external observers by the intensity of the laser dropping.

Both of these effects are essentially exponential in nature, so very 
rapidly the image red****fts and dims to obscurity.  In reality, only a 
finite number of photons are emitted before the object passed through 
the event horizon, and that dimming effect means that at some point, 
very soon, the last photon to be emitted the horizon was hit reached 
distant observers.  So in reality there is no fading image that is 
always there; it rapidly disappears forever.

But remember we're talking about the photons the object emitted, not the 
object itself.  Distant observers can't tell how far away the object 
"really" is or how fast it's "really" going, since those concepts aren't 
meaningful in arbitrary spacetimes in general relativity.  So all these 
distant observers are relying on is the _image_ of the object, not the 
object.  So what they see doesn't really say much of anything about what 
the object itself actually experiences.

This is made even more apparent in a case where one observer goes 
through an event horizon and can by definition never return; even if 
there weren't a singularity on the other side, there's no possible way 
that two observers separated by a horizon can say anything about the 
others' status.  It's essentially a meaningless question, along the 
lines of, "What is one mile north of the North Pole?"

> So, (1) how long does it "really" take to fall
> into the event horizon and then hit the singularity,
> and (2) what is the correct way to ask question (1)?

You'd have to say what you mean by "really."  The only reality of 
comparing distances and velocities in general relativity is locally, so 
the only "real" experience is that of the object itself -- that is, if 
the object falling into the black hole is itself an observer.  In that 
case, the best way of measuring how long it takes for him to hit the 
singularity is by his own watch, something physicists called "proper 
time."  By that measure, the answer is about 10 us per solar mass of the 
black hole.

As is hinted by the twin paradox, firing your engines actually 
_accelerates_ your demise, as the geodesic (freefall trajectory) is the 
path through spacetime that maximizes proper time.  So under no 
cir***stances can you increase your freefall time, though you can make 
death come faster.

Hopefully that answers both questions.

> I'll give (1) another try:
> 
> If I drop a particle into a black hole from somewhere in
> the neighborhood but well outside the event horizon, then,
> from the particle's perspective it will drop through
> the event horizon and hit the singularity in a
> finite period of time.
> 
> But, what if I send a clock signal after it on a laser
> beam, a laser fla****ng once a microsecond? How many
> clock pulses will pass the particle (1a) between
> being dropped and passing the event horizon and
> (1b) between passing the event horizon and hitting
> the singularity?
> 
> I expect the frequency of the clock pulses to increase
> as the particle drops (in the particle's frame) because
> of gravitational blue ****ft. The frequency may even
> approach infinity as the particle approaches the
> singularity, but it does not necessarily mean that
> the integral of the frequency at the particle over
> the proper time of the particle will be infinite.
> 
> If the answer to either (1a) or (1b) is "infinitely
> many clock pulses", then the particle never gets to
> where it's going, from the perspective of the outside
> world.

It depends on the specifics, but the short answer is, no, the infalling 
observer will not experience an infinite number of clock pulses.  He'll 
experience the same number of clock pulses as indicated by his watch, 
plus or minus a bit depending on the quantitative details.  The later 
ones will be more blue****fted than the earlier ones, but that's about 
it.  The FAQ mentioned above goes into some detail about the general idea.

Remember, nothing is different _locally_ about the event horizon.  With 
a big enough black hole, you could pass through the event horizon and 
not even know it.

-- 
Erik Max Francis && max@[EMAIL PROTECTED]
 && http://www.alcyone.com/max/
  San Jose, CA, USA && 37 18 N 121 57 W && AIM, Y!M erikmaxfrancis
   I only drink to make other people seem interesting.
    -- George Jean Nathan