Thought experiment:
Imagine a desk, with a light bulb on the right side, and a mirror placed upon the left side.
Then think about this desk falling towards the event horizon of a black hole.
The bulb makes a brief flash, once every 3 seconds or so, and you are placed, as a distant observer, so that you can see this flash, and briefly afterwards, due to the delay in the light travelling towards the mirror, you see the reflection of the flash from the mirror.
Diagram
A-slowly flashing light bulb.
B-mirror
C-distant observer, considered unaffected by black hole’s time dilation.
D=distance between light bulb and mirror according to the white mice.
d=Observed distance between A and B, by distant observer C
T=time taken between light flash, and light reaching the mirror, from the point of view of the white mice on the desk.
t=time between light bulb flash being seen by C, and reflection from mirror(B) being seen by C.
Time is dilated increasingly, for the desk, as it approaches the event horizon, and let us presume that, for this thought experiment, that it has reached the point where time is dilated by a factor of 2, for the desk; that is for every second that the distant observer experiences, the desk, or let’s say some white mice in a protective cage upon the desk, experiences two seconds.
One of the axioms of relativity is that light is always measured as travelling at the same speed, where ever you are in the universe, and under any conditions, that is about 300,000,000meters per second.
Therefore if the desk experiences a time dilation factor of 2, then from the distant observers point of view,everything at the desk will be slowed down by a factor of 2, the time between the flash from the bulb and the reflection of the flash from the bulb will also increase by a factor of 2.
So therefore, the speed of light, as measured by the white mice would be D/T which should equal 300,000,000m/s, roughly.
But if C tries to measure the speed of light by looking at the desk set up, he will calculate it by saying speed of light=d/t which according to the relativity axiom should also equal 300,000,000m/s
And as t is twice as long(big) as T then for D/T to equal d/t to equal 300,000,000m/s
d has to be twice as large too, to keep the same value(ratio).
Therefor, if light is always measured as having the same speed, the length of the desk has to be observed as twice as long(in this case), or else an observer will calculate an incorrect value for the speed of light.
So the general application is that an object looks longer by the same factor by which time is dilated for that object, as observed by a distant observer, like C. And if this were applied between ever two points on an object like the Earth, then the whole object should have the appearance of increased width by the same factor. And for a time dilation factor of f, I suppose the apparent size increase of an object should be f squared, ie in both x and y dimensions.
So if this applies to objects on a planet or ordinary star. Then, due to time dilation on the surface, two cities on the Earth may measure as being separated by L meters, by the people that live there, but from space the two cities will appear to be separated by L+x, ie slightly further apart, and if this was applied to every point on the Earth, then the whole earth would appear bigger by a factor of f squared too.(if f were the time dilation factor on the Earth's surface)
As applied to the Sun, which has a surface time dilation factor of 2 parts per million, then the Sun should look 2784 meters wider, for a distant observer, than it would for an observer close up.
That is, observed width of Sun, from a distance=(1000,002/1000,000)*(width of Sun measured close up)
Black holes:
As for black holes; if you have a collapsing star, ie a ball of collapsing matter, you will have huge time dilation factors inside. Maybe time dilation would level out towards the middle though.
If you were to see the collapsing matter ball as an infinite number of shells, starting with the matter in the middle and extending outwards, increasing the radius of the shells, then you could apply the Gravitational Length Dilation(GLD) theory to every pair of points on those shells, so what you end up with is what would appear as a greatly enlarged apparent ball, of very dark matter.
So from the outside you would have what appeared as a large dark ball of matter, but it wouldn't just appear that way, it should behave that way, as light paths just show what is happening to information pathways, like for gravitational information.
But if you were to fall towards this dark star, your own time dilation would increase, and thus the dark star of collapsing matter would decrease, in apparent size, relatively, and so the ball would shrink away from you, until you hit it, or until Hawking radiation evaporated you. Which would happen very quickly for you, and the rest of the collapsing matter, as the rest of the Universe speeded up, as far as you would be concerned. Millions of its years passing for each of your seconds.
There is also this thread I started on the BAUT forum HERE
where we talk about the apparent magnification if you just look at light paths leaving the Sun(or other objects). As you can see the solid green line is the path proposed, but the distant observer sees the point on the Sun's surface along the dotted line.
Also, there is a page HERE where the person talks about soley measuring distances by the wavelength of the light you receive. So if you receive red shifted light on Earth, from the Sun, then that wavelength x, is the same distance for the wave when it left the Sun, so again, gravitational magnification.
He also seems to think that gravitational magnification combined with time dilation is the reason for the flat rotation curves of distant galaxies, thus doing away with the need for Dark Matter.