Dark matter g-field due to daughter universes linked to black holes...A conjecture.

Below is an excerpt from a quite speculative model I've been working
on for years and recently put up on my website, in all its glory...
:-]
While possibly "...not even wrong...", it may at least have value as
a stimulant to 'crazy' physics in the sense of Bohr and Pauli, around
which might coalesce better and, currently, somewhat estranged
mainstream ideas in theoretical physics:

"BLACK-HOLE-MEDIATED DAUGHTER-UNIVERSES AS SOURCES
OF 'DARK MATTER' GRAVITATIONAL POTENTIAL (DMP, = -v^2),
PROPAGATING BACK INTO OUR UNIVERSE. THE LARGE NUM-
BERS HYPOTHESIS REVISITED.

Where...
The total black hole (bh) mass interior to a galactocentric spherical
surface, with radius r, varies as DMP^2, or v^4. I explore a model,
which contains some changing 'constants', giving current universe
age as 13.82 Gyr, very near the recent results from WMAP (which
gives a best fit age of 13.7 Gyr.), and which also yields an unusual
'Klein-Gordon' type equation relating the mass of a bh and that of the
DU it links to. The resulting 'dark matter'-enhanced velocity field
corresponds closely with the observed flat velocity curves of spiral
galaxies, as an example.


A. OVERVIEW.
In the following I present a very incomplete model which nevertheless
has a number of intriguing points of contact with the real world and
with
several outstanding problems in astrophysics. Our universe would be
one of an infinite sequence of proliferating, branching universes,
per-
haps comparable to an infinite network of brane-universes. While
young, our universe would be typical in that each black hole in it
would
connect to a separate, unique baby or daughter universe. In this re-
spect, the model is a distant relative to the old Einstein-Rosen
Bridge...
where passage through the bh brings us to another part of our universe
or to another universe entirely, via a "white hole". However, in the
cur-
rent model, each baby universe IS the 'white hole', on the -other- end
of
a bh bridge, while the bh itself lives in a parent universe one step
back
in the sequence.

By extension, we would then live in but one of many daughter universes
(DUs) connected to and expanding 'alongside' another parent-universe.
This relationship continues without limit upward through super parent
uni-
verses, but not downward. An apparent conservation of fundamental
fermions (or more precisely, their wavefunctions) falling into and
through
bh's constrains the maximum number of daughter and grandaughter uni-
verses 'below' us. The total numbers of such particles entering a bh
must be identical to the numbers of same-class-fermions emerging in
the
resulting DUs and cannot be subdivided arbitrarily. I suspect that
this
last may be related to a rough equality between a universe's
'cross-sec-
tion', as it were, and the total sum of the 'cross sections' of its
stable bar-
yons, and that this may be connected to the Holographic Principle of
G. 'tHooft, L. Susskind and others (see footnote #3 at this article's
end).

The model is driven by a large numbers hypothesis with certain fund-
amental 'constants' changing from initial setpoint values at
time-zero.
It needs to be said that variable fundamental parameters, per se, are
less significant than those which are actually dimensionless, such as
particle mass ratios and ratios of strengths of interactions such as
the
gravitational fine structure constant.

While G, Newton's constant, and Mpl, the Planck mass, are true con-
stants, some parameters would change as shown below:

@t_o - - - - - - - - - - - - - - - - - present - - - - - - - - -
- - - - - in futu
__________________________________________________ ____
Mp~Mpl - - - - - - - - - - - - - - Mp~10^-27kg - - - - - - - - - -
- decreases
Me~Mpl - - - - - - - - - - - - - - Me~10^-30kg - - - - - - - - - -
- "
hbar~10^-15 j*s- - - - - - - - h-bar~10^-34 j*s - - - - - - - - -
- "
Rp~5470m - - - - - - - - - - - -Rp~10^-15m - - - - - - - - - - - -
"
Rpl~5470m - - - - - - - - - - - Rpl~10^-35m - - - - - - - - - - -
- "
Co~10^-11m/s - - - - - - - - - Co~3*10^8m/s - - - - - - - - - -
-increases
Ru~5470m - - - - - - - - - - - -Ru~10^26m - - - - - - - - - - - -
- "
Mu~Mpl - - - - - - - - - - - - - - Mu~10^53kg - - - - - - - - - - -
- "
hbar*Co/G*Mp*Me..(reciprocal of 'grav'l fine structure constant)...,
~unity - - - - - - - - - - - - - - - 10^41 - - - - - - - - - - -
- - - - - - "

NOTE:
While it does not seem required within the model, it seems possible
that,
additionally, the ratio of the proton to the electron mass increases
from
near unity at t_0, to ever larger values over time, thus:
Mp/Me~unity - - - - - - - - - - -Mp/Me~1836 - - - - - - - - - - - -
increases .

(Mp, Me, and Mu are proton, electron and universe masses. hbar is
Planck's constant/2 pi. Rp, Rpl are proton and Planck radii and Ru is
universe radius-of-curvature. Co is vel. of light. Mpl is
~2.17*10^-8kg.)

Regardless of its position in the postulated infinite sequence of
universes,
the mass of any universe is always:

Mu = Mpl^4 / (Mn^2 * Me) or equivalently
= h-bar^2 * Co^2 / (G^2 * Mn^2 * Me) ,

in the current values of fundamental parameters of that particular
uni-
verse.

[Note, Mn is approximately the nucleon mass. Thus, while it could
be the proton mass or the neutron mass, it could arguably be the sum
of the proton and the electron masses. As it stands, the model is not
clear enough to resolve this.]

Radius of curvature of universe is always:

Ru = 2 G * Mpl^4 / (Mn^2 * Me * Cd^2) or
= 2 hbar^2 / (G * Mn^2 * Me). See (8) & (9) below.

It is clear that if the above is at least approximately correct, that
for
Ru to increase at all over time, there must be commensurate change
on the right hand side of the relations.

The particular large numbers hypothesis here states that Ru is always

= {[hbar*Co / (G*Mn^2)] * 2[Mn/Me]} * {hbar / (MnCo)} ,

where the factor inside the first braces is the reciprocal of the
gravita-
tional fine structure constant multiplied by twice the
nucleon-electron
mass ratio. The factor in the second braces is the Compton wavelength
of the 'nucleon'.

Note that 2G * Mu / Ru = Co^2 at all times, which is a defining
Schwar-
zschild criterion for black holes.

Minimum (ie: stellar) mass of gravitationally formed black hole, the
most
extreme end state of a collapsar...

[Mbh = Mpl^3 / Mn^2 = hbar^2 * Co^2 / (G^2 * Mn^2 * Mpl).

Currently [Mbh = 3.681 * 10^30 kg., or ~1.85 Msol in our universe.
This
increased from ~Mpl @ t_0, and will increase in the future. I
speculate
that [Mbh is also an index of physically possible stellar masses over
cos-
mic time. Thus stars on average would have had smaller masses in the
past. Due to an ever decreasing gravitational-fine-structure
'constant',
alpha_g = G*Mn*Mn / hbar*Co, they will have to reach ever greater
masses in the future in order for resulting pressures and temperatures
to overcome proton-proton repulsion, initiating thermonuclear regimes.
This means that the formation masses of typical proto-stars must in-
crease indefinitely over cosmic time. It follows also that no
mini-bhs with
masses [Mbh would exist in such a universe (with the brief exception
of those forming initially at the centers of massive stellar cores
which are
collapsing to form bhs with masses = or [Mbh.) The null result of
searches for Hawking signatures of exploding mini-bhs in the universe
is consistent with this......"

snip

For the following, Md and Rd are, respectively, effective mass and
radius
of curvature of daughter universe DU, and r is the radius of a
galacto-
centric sphere in our universe. Also, the 'DU' being considered is
act-
ually the net, collective effect of all the smaller DUs linked to all
the
individual black holes inside r, acting non-linearly, as though they
were
all located and propagating back through a *fictitious* super bh at
the
center of the galaxy:

"With that caveat, it is worth noting that virtually -all- the Milky
Way's bhs
would likely reside within a distance of ~200,000 LY (=1.892*10^21m)
with a resultant net DU mass Md = 9.61*10^42 kg and an Rd equal to
5.25*10^22 m, and so would give the following total potential (from
both
normal and 'dark matter') at that distance, using (11):

Thus: normal potential + DMP =
- G*Mgal / r - 2*G*Md/(r+Rd), or...

normal + dark matter potential =
- G*(M_stars+gas) / r - 2G*(9.61*10^42kg) / (r + 5.25*10^22 m).

Letting M_star+gas = ~4*10^41 kg, and r = 1.892*10^21m gives a total
potential TP

- (118,700m/s)^2 - (153,500m/s)^2 = - (194,000m/s)^2.

The first term on the left is due to normal matter deep inside r, and
the
larger second term is from the DU-generated potential, only attenuated
somewhat at r due to its unusual keplerian nature. The values of
M_star
+gas, and especially the number and distribution of bhs in our galaxy
are not well known, so this kind of calculation can only have the
crudest
back-of-the-envelope value at this time. Furthermore, even the
orbital
parameters of nearby satellite galaxies like the Large Magellanic
Cloud
are currently not known well enough to provide a clear 'pass or fail'
test
of this model. Yet, the above result is broadly compatible with the
gen-
eral trend of published observations in the literature on the
distribution
of dark and normal matter in galaxies and galaxy clusters.

Incidentally, circumstantial support for this posited link between
black
hole content of a galaxy and its DMP is given in a paper by A. Ferrara
and E. Tolstoy, "The role of stellar feedback and dark matter in the
evo-
lution of dwarf galaxies", 2000MNRAS.313..291F, which noticed a tight
correlation between dark matter content and metallicity in dwarf gala-
xies. Here the point is that metallicity is a fair index of bh
content since
metals are largely broadcast into the interstellar medium by the same
supernova events which often create bhs...."

It must be clear to the reader by now that I have rushed in where
angels
fear to tread! The full text of my rather loose model can be seen at

http://home.earthlink.net/~stargene/

Cheers,
Gene