Black hole mass-sigma correlation

In article ,
(Hans Aberg) writes:

There is a common misunderstanding in this. According to the
cosmological principle the universe looks the same everywhere, in
particular it has the same density everywhere. Therefore it is
misleading to think of the universe as an expanding blob with an outer
edge. There is no such edge.

The reasoning I gave would assume that in the very large scale, the
universe is not homogenous. That might be the case if the universe
expansion is accelerating in later times (alternatively slowing down at
large distances from us). If the acceleration rate is the same in all
directions from us, one could not still assume that the universe is
homogenous, as it might mean that we are in the center.

I have a vague memory that the cosmological principle you mention, that
the universe looks the same everywhere was based on a homogenously growing
(non-accelerating) universe. When so there is this acceleration
phenomenon, one should be somewhat cautious about how that principle is
carried over.

A universe which is homogeneous and isotropic can---just kinematics, no
dynamics or physics---can be static, expand or contract and, if
expanding or contracting, then the rate of this can either be speeding
up or slowing down. If we assume that the universe is accelerating,
then in some sense the rate of expansion of distant parts of the
universe is slower SINCE WE ARE SEEING THEM AS THEY WERE LONG AGO, but
this has nothing to do with the---rather independent---question of
whether the universe is homogenous on very large scales.

My standard reference to clear up questions about such topics is Edward
Harrison's COSMOLOGY: THE SCIENCE OF THE UNIVERSE. There is a chapter
entitled "Expansion".

In article , Ulf Torkelsson
wrote:

The reasoning I gave would assume that in the very large scale, the
universe is not homogenous.

That may be a valid assumption, but according to existing observations it
is fairly homogeneous on the largests scales that have been studied.

The formula you gave, GM/(c^2 r), would give hints on how big a
cosmological blob might become, as it should set a limit as GR forces grow
strong.

One would have to look beyond that limit to tell whether there is
something beyond our local blob.

That might be the case if the universe
expansion is accelerating in later times (alternatively slowing down at
large distances from us). If the acceleration rate is the same in all
directions from us, one could not still assume that the universe is
homogenous, as it might mean that we are in the center.

It might mean, but that would put us in a very special position, which
most of us would consider unlikely.

If the expansion acceleration rate is the same in all directions. Are
there observations confirming that?

I have a vague memory that the cosmological principle you mention, that
the universe looks the same everywhere was based on a homogenously growing
(non-accelerating) universe. When so there is this acceleration
phenomenon, one should be somewhat cautious about how that principle is
carried over.

No, the cosmological principle does not rely on any assumption about the
time-dependence of the expansion. It does require that the expansion
progresses at the same rate everywhere at the same time, but the
time-dependence could be anything that could be generated by an equation
of state and a dynamical theory such as GR.

This is a problem, we do not know what the universe looks now, only what
it looked like when the light was sent out.

So I see how you can push through the argument by assuming that the
universe we do not observe is uniform at any given time, but it
accelerates with time, explaining what we actually can see. (Actually, I
was well aware of this argument since before, but overlooked it as I was
thinking too much on other explanations :-).)

Hans Aberg

In article , Ulf Torkelsson
wrote:

The reasoning I gave would assume that in the very large scale, the
universe is not homogenous.

That may be a valid assumption, but according to existing observations it
is fairly homogeneous on the largests scales that have been studied.

The formula you gave, GM/(c^2 r), would give hints on how big a
cosmological blob might become, as it should set a limit as GR forces grow
strong.

One would have to look beyond that limit to tell whether there is
something beyond our local blob.

That might be the case if the universe
expansion is accelerating in later times (alternatively slowing down at
large distances from us). If the acceleration rate is the same in all
directions from us, one could not still assume that the universe is
homogenous, as it might mean that we are in the center.

It might mean, but that would put us in a very special position, which
most of us would consider unlikely.

If the expansion acceleration rate is the same in all directions. Are
there observations confirming that?

I have a vague memory that the cosmological principle you mention, that
the universe looks the same everywhere was based on a homogenously growing
(non-accelerating) universe. When so there is this acceleration
phenomenon, one should be somewhat cautious about how that principle is
carried over.

No, the cosmological principle does not rely on any assumption about the
time-dependence of the expansion. It does require that the expansion
progresses at the same rate everywhere at the same time, but the
time-dependence could be anything that could be generated by an equation
of state and a dynamical theory such as GR.

This is a problem, we do not know what the universe looks now, only what
it looked like when the light was sent out.

So I see how you can push through the argument by assuming that the
universe we do not observe is uniform at any given time, but it
accelerates with time, explaining what we actually can see. (Actually, I
was well aware of this argument since before, but overlooked it as I was
thinking too much on other explanations :-).)

Hans Aberg

In article , Ulf Torkelsson
wrote:

The formula you gave, GM/(c^2 r), would give hints on how big a
cosmological glob might become, as it should set a limit as GR forces grow
strong.

One would have to look beyond that limit to tell whether there is
something beyond our local glob.

This is rather the length scale at which the curvature of space-time
becomes
significant. If we use the critical density of the universe 1.88e-26
kg/m3, then
this lenght scale becomes of order

r = (c^2/G rho)^(1/2) = 3e26 m = 1e10 ly

which is about the size of the observable universe.

I can think of two possibilities: Either the mass density you quote
remains constant throughout the universe, in which case I figure
time-space will eventually (if the region where this is true is
sufficiently large) curve so much that in effect it is a black hole, in
effect the whole universe, as nothing can escape it. Or, moving outwards,
the density must somewhere decrease, bent by GR effects.

I recall that one turned the Hubble telescope to an area that formerly
looked pitch black, and one found a lot of tiny galaxies there. I figure
those galaxies are well within the limit you give above (otherwise we
would probably have heard more about it in the newspapers :-)!). But
perhaps better telescopes could admit one to look beyond that limit (a
selling point for better telescopes?). I think that the redshift argument
says that galaxies sufficiently distant will redshift so much that they
cannot be observed. But if there is a local glob structure, one should be
able to look beyond it to observe galaxies with less redshift.

The big bang theory assumes that there is only one glob, plus that the
expansion of visible matter is caused by a big bang. In a glob theory, one
would still have to find an explanation of the expansion of visible
matter.

Hans Aberg

In article , Ulf Torkelsson
wrote:

The formula you gave, GM/(c^2 r), would give hints on how big a
cosmological glob might become, as it should set a limit as GR forces grow
strong.

One would have to look beyond that limit to tell whether there is
something beyond our local glob.

This is rather the length scale at which the curvature of space-time
becomes
significant. If we use the critical density of the universe 1.88e-26
kg/m3, then
this lenght scale becomes of order

r = (c^2/G rho)^(1/2) = 3e26 m = 1e10 ly

which is about the size of the observable universe.

I can think of two possibilities: Either the mass density you quote
remains constant throughout the universe, in which case I figure
time-space will eventually (if the region where this is true is
sufficiently large) curve so much that in effect it is a black hole, in
effect the whole universe, as nothing can escape it. Or, moving outwards,
the density must somewhere decrease, bent by GR effects.

I recall that one turned the Hubble telescope to an area that formerly
looked pitch black, and one found a lot of tiny galaxies there. I figure
those galaxies are well within the limit you give above (otherwise we
would probably have heard more about it in the newspapers :-)!). But
perhaps better telescopes could admit one to look beyond that limit (a
selling point for better telescopes?). I think that the redshift argument
says that galaxies sufficiently distant will redshift so much that they
cannot be observed. But if there is a local glob structure, one should be
able to look beyond it to observe galaxies with less redshift.

The big bang theory assumes that there is only one glob, plus that the
expansion of visible matter is caused by a big bang. In a glob theory, one
would still have to find an explanation of the expansion of visible
matter.

Hans Aberg