Let's get down to the nitty gritty here.
At 12:20 PM 12/26/2012, David Roberson wrote:
Is the event horizon of a black hole considered an observer relative
location? We, who are at a very large distance relative to a black
hole see the event horizon as located a finite distance from the
center of the star. If another observer happens to be closer to the
same hole, does he detect it as somewhat nearer to the center of the hole?
No. Here is how I come up with that. I read "closer" as still being
in the same inertial frame of reference, and that frame of reference
includes the black hole. So the two observers and the black hole
location are stationary with respect to each other. That requires
some kind of restraining structure, we will make one out of
unobtainium, if I have any left over from my other project.
Obviously, the unobtainium structure is quite large, it surrounds the
black hole and is thus not going to fall into it. No touchie, though.
Before the object reaches the black hole, it emits a photon toward
the observers. That photon travels at the speed of light. As it
climbs the gravity well, it red-shifts, but its velocity doesn't
change. Because the red shift depends on the relative position of the
point of emission, and the point of observation, and if one knows the
original frequency of the light, and the gravitational field, one can
determine the location of the object when the light was emitted.
Let's assume that there are two photons, emitted together, parallel
to each other, and one is captured by the inner observer, and one by
the outer. The outer capture, of course, because of the time it takes
the photon to travel to the outer station.
But both stations will calculate the same position for the emitting
object. However, that's a calculated position.
The question implies a method for determining the position of an
object. What do we mean by "location"? How do we determine it? How do
we "see" an event horizon? What do we mean by "seeing" the position
of the object?
A black hole cannot pass any light from behind it. Light that grazes
it will be curved, toward the object. Gravitational lensing. If
there is a bright background, with collimated light, the black hole
would appear, relatively close to the hole, to be larger than it is,
because grazing light would converge. It would come to a focus point.
Beyond that point, the black hole would be only a darkening of a
region. Light that grazes would be blue-shifted as it approaches the
black hole, and red-shifted as it continues past it.
Okay, a thought experiment. We have a very good telescope. We can see
two targets on the object, and we "see" the distance of the targets
by how far apart the targets appear, we can measure that, and use the
angular distance to determine the physical distance.
Problem is, that damned gravitational lense. Suppose the targets are
equidistant from the "center line," i.e., the line between the
observer and the black hole, and the object is held at a distance.
Long strong string, out to our unobtainium structure. Unobtainium
twine, special manufacture.
How do the two observers see the object?
Well, the light emitted from the targets is lensed. It will be bent
toward the centerline. The targets will appear to be farther apart
than they are. Our rangefinder will "see" the object as closer than
it is. It seems that this effect will increase with distance, as the
light curves more. So the further observer will see the object as further out.
But this is a mere optical effect! The method of determing distance
by observing the red shift of light with a known emission frequency,
through a known gravitational field, would not be fooled.
Look, this is really outside my field. There are many ways to get an
analysis like this wrong. I have about 10% confidence that I got it right.
I have an interesting thought experiment that depends upon the
answer to this question. My suspicion is that the perceived horizon
location does depend upon the exact location and most likely motion
of the observer. Has anyone had an opportunity to actually
calculate this effect?
My suggestion is obvious. Nail down what you mean by "exact
location." Motion of the observer tosses another complication into
the picture, relativity, time dilation, yatta yatta.
Gotta watch out for tought experiments. They often reveal more about
how we think than they reveal about reality, and if our thinking is
not really careful and solid, well, you can get more stinkin from
thinkin than from drinkin, an old friend used to say.
