Are Black Holes Dark Matter factories?

In article ,
Phillip Helbig---remove CLOTHES to reply wrote:
[...]
"Dark energy" is a newfangled name for the cosmological constant. As
Sean Carroll points out, a better name would be "smooth tension".

Ooh, nice name.

I hereby claim the right to "Smooth Tension" as the name for a
progressive-rock group, if I ever get around to founding one. I can see
it written on both bass drums now. :-) (Which reminds me, I believe
that guitarist Brian May of Queen was once a student of astronomy but
gave it up when he started making money with Queen. Anyone who knows
details can provide them to me via email.)

A friend was setting up a violin, etc. performing group and
asked around for suggestions of names ("string beings" was my
favorite among her candidates, though she somehow didn't like
that one). I suggested "Robin K. and her 11-dimensional strings".
She didn't go with it, but I still hope someone to see someone
use a name like that someday.

[Mod. note: OK, I feel further discussion along these lines would be
best in some other newsgroup, though I have to say I'm not sure what
-- mjh]

Hans Aberg wrote:

In article , Ulf Torkelsson
wrote:



This even distribution, not attached to objects, is also what causes
problems with the cosmological constant, producing unstable universes.





I cannot see that this is a problem, since we observe the universe to be
expanding just like we expect from the Friedman-Robertson-Walker model.



This refers to the problems, which I recall you mentioned before, that a
non-zero cosmological constant causes exponential growth in the universe
if it is not exactly right. I do not recall the details.

Well, we observe that the universe is in a state of exponential expansion.


From what one knows about other physics, such an instability seems
unlikely. There ought to be a mechanism that makes the universe to hang
together and adjusts appropriately, even if the masses varies. That is
just a hunch.

We do not observe a static universe, so there is no reason to expect
this kind
of fine-tuning.



Then, if one adds an anti-gravitational "levity" force to GR, that makes
the new theory look more like some kind of dual to QM. Its distance
formula should be so that in short distances it is negligible relative
gravity, but in long distances, it should be able to counteract the GR
GM/(c^2 r) asymptotic formula that Ulf Torkelsson before described here.



I try to think it in terms of the Lagrangian used to create the
Einstein-Hilbert equation of GR. The scalar curvature and the
energy-momentum pushes it one direction. The cosmological constant is a
component that pushes it the other direction. The EM components can push
it either direction, though.

The last statement is confusing. EM could mean two things here, either
radiation, which has a positive energy density and pressure, and which
therefore contributes to the attractive gravity, or you could think of
electrostatic forces, which will contribute with a repulsive force if there
is a net charge in the universe, but otherwise the effect of the
electrostatic
forces will be negligible on the global scale.


I got the Lagrangian to
L := s_g + g(F, F) + sum_j(g(P_j, P_j) + m_j^2 + e_j g(P_j, A))
where s_g is the scalar curvature, F the EM two-form, A the EM potential,
and P_j the energy-momentum and e_j the electric charge of the particles.

You seem to write down a Lagrangian for the particles in the universe,
rather
than a Lagrangian for the universe itself. This is not an appropriate
way to do
cosmology, since the expansion of the universe is not about the motion
of the
particles, but it is about the expansion of space-time itself, thus you
should rather
start from the Hilbert action for the metric. A good source for
different ways
of deriving the equations of general relativity is Misner, Thorne & Wheeler
"Gravitation", in particular Box 17.2.




It is better to note that
in general
relativity the source of the gravitational field is rho + 3p, where rho
is the
energy density and p is the pressure. Now, quintessence can be thought of
as a field with p = w rho, where -1/3 w = -1. The equality is true if we
have a pure vacuum energy, that is a cosmological constant. Since rho must
be positive, we see that the gravitational field reverses its sign and
becomes
repulsive if it is dominated by quintessence.



(Sorry for my poor memory; I do not have reference books where I sit.) The
Einstein-Hilbert cosmological constant I recall to be something that is
added to the equation that results after the metric variation. Then I do
not immediately see what it should looks like before the metric variation.
Perhaps you can help out here?


I am afraid not, but my point was that it is possible to either think
of the
cosmological constant as a constant that appears in the field equations,
or as
a fluid with an odd equation of state, and thus it enters directly into the
energy-momentum tensor. The latter way of thinking means that it becomes
one extreme case of a larger class of fluids that we call quintessence.

Ulf Torkelsson

Hans Aberg wrote:

In article , Ulf Torkelsson
wrote:



This even distribution, not attached to objects, is also what causes
problems with the cosmological constant, producing unstable universes.





I cannot see that this is a problem, since we observe the universe to be
expanding just like we expect from the Friedman-Robertson-Walker model.



This refers to the problems, which I recall you mentioned before, that a
non-zero cosmological constant causes exponential growth in the universe
if it is not exactly right. I do not recall the details.

Well, we observe that the universe is in a state of exponential expansion.


From what one knows about other physics, such an instability seems
unlikely. There ought to be a mechanism that makes the universe to hang
together and adjusts appropriately, even if the masses varies. That is
just a hunch.

We do not observe a static universe, so there is no reason to expect
this kind
of fine-tuning.



Then, if one adds an anti-gravitational "levity" force to GR, that makes
the new theory look more like some kind of dual to QM. Its distance
formula should be so that in short distances it is negligible relative
gravity, but in long distances, it should be able to counteract the GR
GM/(c^2 r) asymptotic formula that Ulf Torkelsson before described here.



I try to think it in terms of the Lagrangian used to create the
Einstein-Hilbert equation of GR. The scalar curvature and the
energy-momentum pushes it one direction. The cosmological constant is a
component that pushes it the other direction. The EM components can push
it either direction, though.

The last statement is confusing. EM could mean two things here, either
radiation, which has a positive energy density and pressure, and which
therefore contributes to the attractive gravity, or you could think of
electrostatic forces, which will contribute with a repulsive force if there
is a net charge in the universe, but otherwise the effect of the
electrostatic
forces will be negligible on the global scale.


I got the Lagrangian to
L := s_g + g(F, F) + sum_j(g(P_j, P_j) + m_j^2 + e_j g(P_j, A))
where s_g is the scalar curvature, F the EM two-form, A the EM potential,
and P_j the energy-momentum and e_j the electric charge of the particles.

You seem to write down a Lagrangian for the particles in the universe,
rather
than a Lagrangian for the universe itself. This is not an appropriate
way to do
cosmology, since the expansion of the universe is not about the motion
of the
particles, but it is about the expansion of space-time itself, thus you
should rather
start from the Hilbert action for the metric. A good source for
different ways
of deriving the equations of general relativity is Misner, Thorne & Wheeler
"Gravitation", in particular Box 17.2.




It is better to note that
in general
relativity the source of the gravitational field is rho + 3p, where rho
is the
energy density and p is the pressure. Now, quintessence can be thought of
as a field with p = w rho, where -1/3 w = -1. The equality is true if we
have a pure vacuum energy, that is a cosmological constant. Since rho must
be positive, we see that the gravitational field reverses its sign and
becomes
repulsive if it is dominated by quintessence.



(Sorry for my poor memory; I do not have reference books where I sit.) The
Einstein-Hilbert cosmological constant I recall to be something that is
added to the equation that results after the metric variation. Then I do
not immediately see what it should looks like before the metric variation.
Perhaps you can help out here?


I am afraid not, but my point was that it is possible to either think
of the
cosmological constant as a constant that appears in the field equations,
or as
a fluid with an odd equation of state, and thus it enters directly into the
energy-momentum tensor. The latter way of thinking means that it becomes
one extreme case of a larger class of fluids that we call quintessence.

Ulf Torkelsson

Mick Wilson wrote:

(Gordon D. Pusch) wrote in message ...


Furthermore, even if there were some mysterious process converting normal
matter to "dark matter" that for some mysterious region only functioned
in the inner regions of a black hole's accretion disk, only a very small
fraction of that nascent "dark matter" could escape the black hole via
its jets; the overwhelming majority of the nascent "dark matter" would
simply be swallowed up by the black hole, like any other form of matter.




One issue remains unclear in my mind: dark matter is required to have
virtually zero interaction with either baryonic matter or
electomagnetic radiation; its only profile is a gravitational one,
hence it can be expected to gather in accretion disks. However, dark
matter (to me at least) seems unlikely to lose energy through either
collisions or radiation as rapidly as baryonic matter, and hence to
advect towards the event horizon much more slowly than normal matter.

Therefore, over time, might one expect that black hole accretion disks
become increasingly dominated by dark matter as baryonic matter is
preferentially consumed?

Now, since the dark matter is supposed to be collisionfree, it cannot even
settle down into an accretion disc. For the matter to be concentrated in
the accretion disc, it must somehow dissipate its motion in the direction
perpendicular to the accretion disc, but there is no mechanism available
to do
that.


Further: might a sufficiently dense accumulation, over cosmological
timescales, act as a 'choke' on further accretion and hence (at least
partially) contribute to observed quietening of active galaxies as the
universe has evolved?


It is not clear to me what you have in mind here, but I would say that
it is
rather the opposite, the quietening of active galaxies is rather due to that
they run out of fuel, matter that can easily form an accretion disc around
the central black hole.

Ulf Torkelsson

Mick Wilson wrote:

(Gordon D. Pusch) wrote in message ...


Furthermore, even if there were some mysterious process converting normal
matter to "dark matter" that for some mysterious region only functioned
in the inner regions of a black hole's accretion disk, only a very small
fraction of that nascent "dark matter" could escape the black hole via
its jets; the overwhelming majority of the nascent "dark matter" would
simply be swallowed up by the black hole, like any other form of matter.




One issue remains unclear in my mind: dark matter is required to have
virtually zero interaction with either baryonic matter or
electomagnetic radiation; its only profile is a gravitational one,
hence it can be expected to gather in accretion disks. However, dark
matter (to me at least) seems unlikely to lose energy through either
collisions or radiation as rapidly as baryonic matter, and hence to
advect towards the event horizon much more slowly than normal matter.

Therefore, over time, might one expect that black hole accretion disks
become increasingly dominated by dark matter as baryonic matter is
preferentially consumed?

Now, since the dark matter is supposed to be collisionfree, it cannot even
settle down into an accretion disc. For the matter to be concentrated in
the accretion disc, it must somehow dissipate its motion in the direction
perpendicular to the accretion disc, but there is no mechanism available
to do
that.


Further: might a sufficiently dense accumulation, over cosmological
timescales, act as a 'choke' on further accretion and hence (at least
partially) contribute to observed quietening of active galaxies as the
universe has evolved?


It is not clear to me what you have in mind here, but I would say that
it is
rather the opposite, the quietening of active galaxies is rather due to that
they run out of fuel, matter that can easily form an accretion disc around
the central black hole.

Ulf Torkelsson

In article , Ulf Torkelsson
wrote:

From what one knows about other physics, such an instability seems
unlikely. There ought to be a mechanism that makes the universe to hang
together and adjusts appropriately, even if the masses varies. That is
just a hunch.

We do not observe a static universe, so there is no reason to expect
this kind
of fine-tuning.

I am not speaking about a static universe, but one in which the
cosmological constant can adjust.

I try to think it in terms of the Lagrangian used to create the
Einstein-Hilbert equation of GR. The scalar curvature and the
energy-momentum pushes it one direction. The cosmological constant is a
component that pushes it the other direction. The EM components can push
it either direction, though.

The last statement is confusing. EM could mean two things here, either
radiation, which has a positive energy density and pressure, and which
therefore contributes to the attractive gravity, or you could think of
electrostatic forces, which will contribute with a repulsive force if there
is a net charge in the universe, but otherwise the effect of the
electrostatic
forces will be negligible on the global scale.

The energy density should be what one gets after plugging in an observer
in the stress-energy tensors that result after the metric variation in the
GR Lagrangian. I am thinking about positive and negative contributions in
this Lagrangian itself.

The electrostatic forces should be negligible on the global scale; I just
mention it to illustrate the mathematical principle: I.e., how in
principle get a gravitational constant that varies.

I got the Lagrangian to
L := s_g + g(F, F) + sum_j(g(P_j, P_j) + m_j^2 + e_j g(P_j, A))
where s_g is the scalar curvature, F the EM two-form, A the EM potential,
and P_j the energy-momentum and e_j the electric charge of the particles.
....
You seem to write down a Lagrangian for the particles in the universe,
rather
than a Lagrangian for the universe itself. This is not an appropriate
way to do
cosmology, since the expansion of the universe is not about the motion
of the
particles, but it is about the expansion of space-time itself, thus you
should rather
start from the Hilbert action for the metric. A good source for
different ways
of deriving the equations of general relativity is Misner, Thorne & Wheeler
"Gravitation", in particular Box 17.2.

I am not sure what your comment says here; I merely excluded some of the
standard mathematical details, typical for variational calculus:

One should multiply L above with the metric volume element and integrate,
which gives a new Lagrangian usually written with a script L in print.
After the metric variation, one cancels out some terms using Stoke's
theorem, in the usual way. The stress energy tensors are what results
under the integral sign when the metric volume element has been cancelled,
after some additional symmetrization in the metric variable as motivated
by physical reasoning (as the metric is a symmetric two-tensor).

A good reference for doing this in a coordinate independent notation is
Besse, "Einstein Manifolds" (and those calculations given there apply also
to the Lorentz manifold case).

What is this "Lagrangian of the universe" you are speaking about? Is it
the script L that I indicated above?

(Sorry for my poor memory; I do not have reference books where I sit.) The
Einstein-Hilbert cosmological constant I recall to be something that is
added to the equation that results after the metric variation. Then I do
not immediately see what it should looks like before the metric variation.
Perhaps you can help out here?

I am afraid not, but my point was that it is possible to either think
of the
cosmological constant as a constant that appears in the field equations,
or as
a fluid with an odd equation of state, and thus it enters directly into the
energy-momentum tensor. The latter way of thinking means that it becomes
one extreme case of a larger class of fluids that we call quintessence.

The reason that I was asking is that this then might be another problem
with the cosmological constant: If one expects GR to be completed by a
generalization of the Lagrangian above, the cosmological constant would
then not fit into that picture.

The intuitive physical reasoning that you give for the cosmological
constant would then only serve as a first approximation towards a more
complete theory.

Hans Aberg

In article , Ulf Torkelsson
wrote:

From what one knows about other physics, such an instability seems
unlikely. There ought to be a mechanism that makes the universe to hang
together and adjusts appropriately, even if the masses varies. That is
just a hunch.

We do not observe a static universe, so there is no reason to expect
this kind
of fine-tuning.

I am not speaking about a static universe, but one in which the
cosmological constant can adjust.

I try to think it in terms of the Lagrangian used to create the
Einstein-Hilbert equation of GR. The scalar curvature and the
energy-momentum pushes it one direction. The cosmological constant is a
component that pushes it the other direction. The EM components can push
it either direction, though.

The last statement is confusing. EM could mean two things here, either
radiation, which has a positive energy density and pressure, and which
therefore contributes to the attractive gravity, or you could think of
electrostatic forces, which will contribute with a repulsive force if there
is a net charge in the universe, but otherwise the effect of the
electrostatic
forces will be negligible on the global scale.

The energy density should be what one gets after plugging in an observer
in the stress-energy tensors that result after the metric variation in the
GR Lagrangian. I am thinking about positive and negative contributions in
this Lagrangian itself.

The electrostatic forces should be negligible on the global scale; I just
mention it to illustrate the mathematical principle: I.e., how in
principle get a gravitational constant that varies.

I got the Lagrangian to
L := s_g + g(F, F) + sum_j(g(P_j, P_j) + m_j^2 + e_j g(P_j, A))
where s_g is the scalar curvature, F the EM two-form, A the EM potential,
and P_j the energy-momentum and e_j the electric charge of the particles.
....
You seem to write down a Lagrangian for the particles in the universe,
rather
than a Lagrangian for the universe itself. This is not an appropriate
way to do
cosmology, since the expansion of the universe is not about the motion
of the
particles, but it is about the expansion of space-time itself, thus you
should rather
start from the Hilbert action for the metric. A good source for
different ways
of deriving the equations of general relativity is Misner, Thorne & Wheeler
"Gravitation", in particular Box 17.2.

I am not sure what your comment says here; I merely excluded some of the
standard mathematical details, typical for variational calculus:

One should multiply L above with the metric volume element and integrate,
which gives a new Lagrangian usually written with a script L in print.
After the metric variation, one cancels out some terms using Stoke's
theorem, in the usual way. The stress energy tensors are what results
under the integral sign when the metric volume element has been cancelled,
after some additional symmetrization in the metric variable as motivated
by physical reasoning (as the metric is a symmetric two-tensor).

A good reference for doing this in a coordinate independent notation is
Besse, "Einstein Manifolds" (and those calculations given there apply also
to the Lorentz manifold case).

What is this "Lagrangian of the universe" you are speaking about? Is it
the script L that I indicated above?

(Sorry for my poor memory; I do not have reference books where I sit.) The
Einstein-Hilbert cosmological constant I recall to be something that is
added to the equation that results after the metric variation. Then I do
not immediately see what it should looks like before the metric variation.
Perhaps you can help out here?

I am afraid not, but my point was that it is possible to either think
of the
cosmological constant as a constant that appears in the field equations,
or as
a fluid with an odd equation of state, and thus it enters directly into the
energy-momentum tensor. The latter way of thinking means that it becomes
one extreme case of a larger class of fluids that we call quintessence.

The reason that I was asking is that this then might be another problem
with the cosmological constant: If one expects GR to be completed by a
generalization of the Lagrangian above, the cosmological constant would
then not fit into that picture.

The intuitive physical reasoning that you give for the cosmological
constant would then only serve as a first approximation towards a more
complete theory.

Hans Aberg

Hans Aberg wrote:

In article , Ulf Torkelsson
wrote:



From what one knows about other physics, such an instability seems
unlikely. There ought to be a mechanism that makes the universe to hang
together and adjusts appropriately, even if the masses varies. That is
just a hunch.



We do not observe a static universe, so there is no reason to expect
this kind
of fine-tuning.



I am not speaking about a static universe, but one in which the
cosmological constant can adjust.

I do feel a bit uncomfortable about talking about a varying constant,
which is
one reason that I prefer to talk about quintessence. There has been
quite a bit of
work done in recent years on a scalar field that may be the
quintessence, and thus
generate the current exponential expansion of the universe. If this
field has a
suitable time-dependence, for instance as the result of that it is
tracking another
property of the universe, it may explain both the early inflationary era
of the
universe as well as the current exponential expansion. There are good
popular
introductions to this in the November 2000 issue of Physics World and
January
2001 issue of Scientific American.

[snipping the rest of the article to which I have nothing to add]

Ulf Torkelsson

Hans Aberg wrote:

In article , Ulf Torkelsson
wrote:



From what one knows about other physics, such an instability seems
unlikely. There ought to be a mechanism that makes the universe to hang
together and adjusts appropriately, even if the masses varies. That is
just a hunch.



We do not observe a static universe, so there is no reason to expect
this kind
of fine-tuning.



I am not speaking about a static universe, but one in which the
cosmological constant can adjust.

I do feel a bit uncomfortable about talking about a varying constant,
which is
one reason that I prefer to talk about quintessence. There has been
quite a bit of
work done in recent years on a scalar field that may be the
quintessence, and thus
generate the current exponential expansion of the universe. If this
field has a
suitable time-dependence, for instance as the result of that it is
tracking another
property of the universe, it may explain both the early inflationary era
of the
universe as well as the current exponential expansion. There are good
popular
introductions to this in the November 2000 issue of Physics World and
January
2001 issue of Scientific American.

[snipping the rest of the article to which I have nothing to add]

Ulf Torkelsson

(Hans Aberg) writes:

In article , Ulf Torkelsson
wrote:

From what one knows about other physics, such an instability seems
unlikely. There ought to be a mechanism that makes the universe to
hang together and adjusts appropriately, even if the masses
varies. That is just a hunch.

We do not observe a static universe, so there is no reason
to expect this kind of fine-tuning.

I am not speaking about a static universe, but one in which the
cosmological constant can adjust.

The problem with what you are speaking about is that it is oxymoronic:
The cosmological constant is, by definition, _CONSTANT_. If the C.C. were
to "adjust" or vary in any way, then the covariant divergence of the
stress-energy-momentum tensor would be non-zero, and matter, energy,
and momentum would be created from nothing; this is Considered Bad.
If the C.C. has =ANY= type of "dynamics" at all, it ceases to be a
"cosmological constant," and becomes just one more "matter" field,
and these days is usually referred to as a "quintessence."


I try to think it in terms of the Lagrangian used to create the
Einstein-Hilbert equation of GR. The scalar curvature and the
energy-momentum pushes it one direction. The cosmological constant is a
component that pushes it the other direction. The EM components can push
it either direction, though.

The last statement is confusing. EM could mean two things here, either
radiation, which has a positive energy density and pressure, and which
therefore contributes to the attractive gravity, or you could think of
electrostatic forces, which will contribute with a repulsive force if there
is a net charge in the universe, but otherwise the effect of the
electrostatic forces will be negligible on the global scale.

The energy density should be what one gets after plugging in an observer
in the stress-energy tensors that result after the metric variation in the
GR Lagrangian.

What do you mean by "plugging an observer into the stress-energy tensors"?
This statement sound suspiciously like "technobabble" to me. For one thing,
please note that it is =THE= stress-energy-momentum tensor: singular, not plural.
For another, one does not "plug an observer into it." One can plug "one-forms"
into it, or vectors if one lowers an index using the metric, but an "observer"
is neither a one-form nor a vector. Please explain what you mean by the above
statement.


-- Gordon D. Pusch

perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;'