(Old Physics)
Message-id:

Thank you for your defense of the question, Mr. Jastrzebski.
If Bilge were to answer the question he would probably point out
that the stresses on the shell that would cause it to collapse would
be part of SR-GR. My object in posing it is two fold. First it is
difficult for me to reconcile that the mass of say 10^22 suns would be
equal to a shell a billion LYs in diameter with a mass of about two
pounds per sq ft and a BH with an EH of the same diameter. It just
dosn't seem that time would stop there to an outside observer; it
would just proceed half as fast.

It is more complex than that.

Mass 10^22 suns is about everything that there is in the
universe. This matter if spread relatively uniformly throughout
the space makes the space bulging out everywhere about the same
and this bulging makes the space closed within itself similarly
like bulging of the earth surface makes the earth surface closed
within itself. So there can be no outside observer that could
look at it from outside. We can look at it only from inside.

While we don't have problems with imagining 2D curved surface
of the earth closed within itself it is rather tough to imagine
3D curved space closed within itself. That's why I wrote a whole
article about how we can imagine such thing without getting too
big a headache or even go crazy. It is in my "Einsteinian Gravity
for Poets and Science Teachers" in
http://www.geocities.com/wlodekj/sci/gravity.htm
in section about curved space. If you read it you may share with
me your impressions about style, clarity, possible errors, etc.

Result of all this is that the mass of those 10^22 suns (or any
mass spread uniformly throughout the space) would curve the space
of the universe so that it would be closed in itself (smaller
mass would result in greater radius of curvature according to
formula R=c/sqrt(4 pi G rho) where c is speed of light, G is
Newtonian gravitational constant, rho is density of space). So
formally it would be a BH since light (or anything else) could
never leave it. "Leaving it" wouldn't have any meaning neither
since there is no outside to this space. This is all what there
is: 10^22 suns floating in space that is closed within itself.
You don't need a shell just a space closed within itself. No
outside.

How much the time is dilated in this space while looked at by
the inside observers?

We may recall that there is a fixed relation between the
curvature of space and time dilation. Namely the relative
amount of one is equal to the relative amount of the other.
As I mentioned before this equal amounts are forced on the
universe by its inability to create energy from nothing
(a.k.a. "the principle of conservation of energy").

Mathematicians who call themselves "gravity physicists",
and consequently the astronomers who listen to them since
they can't handle relativity on their own, don't believe that
energy is conserved "in gravity" (actually they say as Bilge
does too, that they don't know what word "energy" means "in
gravity" and so they are not able to say whether it is
conserved or not). So they may have different ideas about the
relation between time dilation and curvature of space than
those expressed here. Actually, assuming that energy can be
created from nothing and destroyed to nothing, they enjoy a
lot of freedom in assuming how much energy may be created
legally form nothing and so for them there are no barriers in
their ideas about the universe.

Those who think that energy can't be created or destroyed
(as I do) don't have this freedom of thought and have to
follow physics that assumes strict conservation of energy
and everything what follows from it. One important result
is the mentioned equality of relative time dilation and
relative curvature of space ((@^2)T/@t@r + 1/R = 0, where
@ is partial, T is proper time, t is coordinate time, r is
coordinate distance, R is radius of curvature of space).

The above is of course not what standard (big bang) cosmology
assumes (since conservation of energy has been dropped from
standard cosmology) and so if you want to know the standard
cosmology's opinion about those things I'm not the proper
authority on this subject. I can only tell you what would
happen in a world in which energy is conserved. If you are
still interested then it would be the following:

When you look through this curved by the presence of matter
space, the farther you look along r the more time dilation
(dT/dt) you see (mathematically you just integrate the above
formula along r). Since you'll see time running slower the
farther you look you'll see also the spectra of galaxies at
those far away places shifted towards red. The astronomers
call the effect "Hubble's redshift" and think that it is
because those galaxies move away, and so they call "Hubble's
constant" the ratio of their alleged "speed of recession" to
the distance (presently about 70 km/s/Mpc).

I call this effect "general time dilation" since it is
always some amount of it in the space. The amount of this
shift per unit of distance from the above relation equals
1/R (so the value of Hubble's constant equals c/R). For the
observed Hubble's constant the radius of curvature of space
of the universe turns out to be R = ~4 Mpc and so it means
that the density of this space is about 6x10^(-27) kg/m^3.

Since this is well within estimates that astronomers do for
the density of the universe we don't need to believe the
astronomers that galaxies move away and instead we may stick
to the idea that energy is conserved. So we have time
dilation forced on the universe by the curvature of space
(and the mention inability of the universe to create energy
from nothing).

One more advantage of sticking to conservation of energy
rather than to the idea that the universe is expanding is
that since the above predicts exponential time dilation
with distance, it simulates not a simple uniform expansion
but accelerating one. Which is observed and for which the
official cosmology needs not only to suspend conservation
of energy but also invent some special forces accelerating
the alleged expansion ("Dark Energy"). But this is common
fate of silly theories: the more facts show up the more
silly the theory becomes until it collapses under the
weight of its own silliness. So we just need to wait for
more facts. BTW "anomalous" acceleration of space probes
Pioneer 10 and 11 is also on the side of conservation of
energy and numerical values fit within several percent.

So that's approximately the answer to your question about
the time dilation in a space containing 10^22 suns :-).

Second, it makes me wonder about the dynamics of quasars
which are believed to generate their light in an acreation disk
around a BH with a mass in the range of a hundred million suns.
Could it be that part of the redshift of quasars is from time
dilation-gravity within this region?

What else do you think it could be? The only thing that
produces redshift (excluding recession of quasars for which
there is no evidence and even as Halton Arp maintains it is
contradicted by observations because of obvious bridges between
them and galaxies with much smaller redshifts) is time dilation.
However except the common (almost Newtonian) gravitational time
dilation (the one that equals Newtonian potential divided by
c^2) there is also, overlooked by astronomers, general time
dilation caused just by the conservation of energy in curved
space at conditions in which Newtonian potential may be zero.
It must have mislead astronomers into thinking that this
redshift (they call it "dynamical friction") is negligible and
they never bothered to calculate it. So the quasars' redshift
might be combination of those two, or even mostly this
neglected so far "general time dilation".

But it has to be analyzed rather by astronomers after they
give up Newtonian prejudices and understand how energy
is conserved in gravity and therefore why there has to be
this "general time dilation". Which won't be an easy project
while most of them think that energy can't be conserved
and moderators don't let to discuss the issue of
conservation considering it "too speculative".

Conservation of energy is "too speculative" for astronomers.
They would rather discuss "dark energy" and "repulsive
gravitational force" (the one that "accelerates" the
"expansion"). So we may need another century to get rid
of all those myths about the universe and to notice that
Einsteinian gravity explained all those things several
generations ago.

-- Jim