Imagine the Sun as it sits in its gravitational field. As light is emitted from its surface, its path is curved by that gravitational field something like this.
The paths of light on this page may be exaggerated to demonstrate the effect.
The light's path is represented by the solid green line.
But to a distant observer, they will see the point of emission, from the Sun, as being along the dotted line. And if this where applied to all the light leaving the Sun, then the distant observer would see a much larger(magnified) Sun.
Where it appears that the Sun should appear about 2 or 3 kilometers wider(and higher), for the distant observer, than it would look(measure) close up.
This matches the idea that magnification is also linked to the apparent speed of light in a time dilated gravitational field.
Imagine a desk sitting on a planet's surface. The planet has no atmosphere, the desk has a light-bulb at one end, and a mirror at the other, so that the light-bulb, and its reflection, can be seen by a distant observer in space.
The bulb flashes on and off, say once a second.
So the distant observer sees the light-bulb come on, and then some time(t) later sees the bulb come on, as reflected in the mirror.
If the area of the desk is time dilated so that it takes light twice the time to get from bulb to mirror, as viewed, and timed, by the distant observer compared to how long a local observer would time it,then I would suggest that the distance between bulb and mirror would be appear twice as far, compared to how a local observer would measure it.
As the the time measured between two points might, for example, be doubled, then the distance between those two objects would have to be doubled, if light were to be calculated as c.
Look at the diagram of the desk again, and as you can see, the light from the bulb and the mirror would appear to be coming along the dotted line, so that the desk would appear longer(and hence wider too).
Time dilation on the Sun's surface is 2 parts per million, and its diameter is 1.392×10
^{9} m.So as light would appear to take 2 parts per million longer to go between any two points on the
surface then I would suggest that the distance between those two points(and any two points)
should appear to be larger by 2 parts per million, also.
In this case the Sun should appear to have a diameter roughly 2784meters larger than it would
measure to someone on(close) to the Sun's surface.
Which corresponds to how much larger the Sun would appear based upon the curvature of the
paths of light leaving the surface.
Black HolesNow consider black holes; stars that have used up all their fuel and are in the state of collapse.
Black holes are said to have an event horizon, from in which no light can escape.
That as matter falls towards this event horizon, it experiences more and more time-dilation,
to the extent that time dilation, at the event horizon, is infinite; ie time there appears to have
stopped for the distant observer.
The event horizon forms a sphere, for the non spinning black hole, and has a radius called
the schwarzschild radius, which is given by the formula
Now if you consider the area just above the event horizon, and treat that as a surface which
would be effected by gravitational magnification, the black hole may well appear to have
roughly the radius given by the schwarzschild radius, for the distant observer, but as one got
closer to the black hole, it would appear to get smaller, and smaller.
Imagine a beam of light entering a black hole, and observers, a, b and c on that path.
The light path in would also be a light path out, so that the area just above the event horizon
would appear along the tangent to that path. ie along the dotted lines.
So that as one progressed from
A(the observer at an infinite distance) who sees the largestsphere, to
B, who sees a smaller sphere to C, who sees an even smaller sphere, and so on.I think that it makes sense that
B, and C would appear along the dotted line, as seen by A; ie the one that leads to the largest sphere.
So as anything which appears to be falling towards the event horizon
(ie like
B, and C being on the first dotted line) see repeated diagram with red dots for where Band
C would be seen by observer at infinity.So all the matter involved in the collapse is seen to be falling into an event horizon, but if one
were to fall into the black hole, then one would see(measure) the whole thing as shrinking.
And as one go closer and closer to the center, one would become more and more time dilated,
so that a few seconds to you, would be experienced as millions(maybe billions) of years by
the distant observer.
Also, for light leaving the small grain of time dilated collapsing star matter, the matter it leaves behind will appear/measure as getting bigger so that I suppose that it warps space less(exerts less of a pull) the further it gets, making it easier for that light to get away. The mainstream view is that a black hole gradually evaporates, over the millions of years, via
Hawking Radiation, but that relies on there being an event horizon.
I think that there probably is a similar process that doesn't rely on an event horizon, which is
called "pre-Hawking Radiation".
And my guess is that black holes are really just grain of sand(Dust?) sized objects, the mass of
multiple suns(or the combination of blackhole masses with super massive blackholes at the
center of galaxies) that are heavily time dilated, and heavily magnified, that evaporate over
the billions of years, via this pre-Hawking radiation, as would anyone who fell in to one.
Anyone who fell into one would be evaporated within a few seconds of their time. There
would be no crossing of any event horizon, for them, or any other matter.
A good thing about this model of black holes, is that one can easily see how angular momentum
(spin) of the object can be preserved, as it is still a mass with volume; where as it is harder to
see how angular momentum would be preserved with a singularity. email: tofunut@googlemail.com |

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