http://garyakent.blogspot.com/2014/03/galactic-gravitational-fields.html part 1
Part 2
Data For M-sigma:
Literature
values:
Mmw = 1.99
x 1042 kg[61],
since Mmw
= Milky Way Mass =
1.00 ×1012 Mʘ and
Mʘ = 1.9891×1030 kg, G
= 6.67384 x 10-11
m3 kg‑1 s-2
parsec = 3.09
x 1013 m = 3.26 light-years
1 ly = 9.4607 × 1015 m
60s/min x 60min/hr x 24hrs/day x 365.25 days/yr = 3.156 x 107
s/yr
Dmw = 110 kly
= 34 kpc [62]
Mbhmw [63] = 4.3
x 106 Mʘ taking Ghez’s30
mid-range value
Mbhmw =
4.3 x 106 Mʘ x 1.9891×1030 kg/ Mʘ = 8.6
x 1036 kg,
Dbulgemw
≈ 10,000 kpc [64] rbulgemw ≈
5,000 kpc
Dbulge σmw
within ± σ of the center ≈
6,827 kpc (± 1 std. deviation or
containing 68.27% of the total stellar population[65]), so
rσ = 3,414 kpc
= 9.98 x 1035 m
M - sigma
characteristic velocity dispersion for the MW,
for the characteristic
velocity of bulge stars in the Milky Way. This is our own galaxy’s
super-massive black hole’s stellar bulge velocity “dispersion” got via the M ‑
sigma diagram and graph at the blog in ref. (74).
Example (2)
By back-solving using standard
Newton/Kepler
rσ = GMbh/vσ2
vσ
↓ G ↓
rσ = [Mbhmw/(1.03
x 105m/s)2 ] x 6.674 x 10-11m3/kg s2 =
rσ = [8.553x1036
kg/(1.03x105m/s)2 ]x6.674x10-11m3/kg s2 = 5.38x1016m
=
1.74 kpc
The value of rσ ↑ where vσ (= “σ”), the
velocity across galaxy bulge fractional radii containing 68% of the stellar
population, which denotes or defines a Gaussian or normal velocity
distribution. This value of r is at 1 standard deviation from the mean velocity
distribution (µ = 0) and it isn’t so very far off, actual rσ ≈ 3.41 kpc (see
ref. 74).
So, these “reverse engineered” calculations are not too far
off, showing that standard Kepler might be used this way. But, the Postulate
can also be used.
From our perspective on Earth, the
distribution can appear Gaussian even though the Milky Way’s bulge is really a
bar[66].
But, being a barred galaxy, use of a simple Gaussian distribution may not be
truly warranted once again, see ref. (74).
Example (3)
Using the Postulate and M-Sigma data:
Mbhmw = vσ2r*/G* by eq. (4)
Mbhmw = (1.03 x 105 m/s)2(1.0
m) /2 x 10‑32 m3 kg‑1 s-2
= 5.30 x1041 kg
vσ ↑ G* ↑
5.30 x 1041 kg/1.9891 x
1030 kg/Mʘ =
2.667 x 1011 Mʘ = σMbhmw
This is Mbhmw
using the Postulate via “σ” or vσ data which is got
from the M ‑ sigma diagram[67] and
the graph at the above blog entry.
Compare with the AVD value,
avdMbhmw = 2.42 x1042 kg =
1.247 x 1012 Mʘ
via the Postulate & AVD
and compare the literature values
Mbhmw = 8.6 x 1036 kg = 4.3 x 106 Mʘ x 1.9891×1030 kg/Mʘ observed
Mmw = 1.99
x 1042 kg = 1.00 x 1012 Mʘ
observed
These postulated values for avdMbhmw
and σMbhmw are not really too large, from
about 1 ¼ to almost 3 times the mass of the entire Milky Way (which is underestimated).
But, after all, we are looking for missing mass. And we got it by using a
somewhat diminutive G* and 2-D adapted Kepler’s laws. This is not an absurd
value. What is absurd is the notion that in over 13 billion years of evolution,
the Milky Way is said to have accumulated a central supermassive black hole
with a mass of only a paltry few million sols.
A. Ghez analyzed Keplerian motion of
inner bulge stars like S-2 and got 8.553 x 1036 kg (4.3 x 109
Mʘ). The Mbhmw
implied by the M-sigma diagram at the blog entry is at least 4 x 1036
kg (2 x 109 Mʘ).
But these values all depend on standard Newton/Kepler. They must grossly
underestimate Mbhmw and all other Ms where black holes
may be involved.
That Ghez’s Mbhmw is so much smaller than the Postulate’s (which uses an
observed value of vσ) our own galaxy’s Mbhmw means that if we
apply the Postulate directly to bulge stars along with the implications of the
M ‑ sigma relation we need better data. But, this is good because “precision
cosmology” must live up to its name and it’s our job.
We wanted a source of Mbh that is
determined by standard Newton/Kepler to compare it with a separate computation
done using the Postulate. We got it. Note that similar considerations will
account for the Magorian relation as well. We found that the Postulate computes
Mbhs that are enormously larger and go a long way toward explaining
Dark Matter. If we iterate the G* computation and pursue a process of
successive approximation, the resulting higher quality G* would further amplify
this result and could account for Dark Matter 100%.
Example
(4) Using the Postulate
Milliparsec, mpc A unit of
astronomical distance equal to 3.0857 x 1013
m or 0.003262 light years
3.156 x 107 s/yr = seconds per
year
Using Ghez’s data[68],
the orbital period P of the best, most typical closely orbiting star, S0-2, is
P = 15.78 yrs = 4.980 x 108s the orbital periapse = Rmin = 0.570 mpc
And the semi-major axis of its orbit is
a = Rmin/(1-e) from the definitions
of ellipse, periapse and eccentricity
=
1.5510 x 1014 m
We’ll take our first approximation to G* as
G* = 2.128 x 10-32 m2kg-1s-2
Adapted Kepler’s 3rd law (Ka), where r = a
KaMbhmw
= 4π2r2/G*P2 = (4π2/G*)(r2/P2)
= (1.855 x 1033m-2kgs2)(1.551
x 1014m)2/(4.98 x 108s)2
= 1.799 x 1044kg , (’’ ’’)/1.9891 x 1030kg/Mʘ = 9.046 x 1013Mʘ
We have the above value and the AVD value
using the Postulate
avdMbhmw = 2.42 x1042 kg =
1.247 x 1012 Mʘ and the M - sigma
value using the Postulate
σMbhmw
= 2.667 x 1011 Mʘ
Whereas Ghez got KMbhmw = 4.3 x 109 Mʘ Using unadapted
standard Kepler’s 3rd (K).
There is nothing so special about σ
and so we should probably favor 2σ or
else r50%
in
computing M - sigma or M - 50% via the Postulate. This would raise or lower σMbhmw somewhat because it
would raise or lower vσ, according to the diagram at the blog entry.
The value for avdMbhmw may be inflated by the presence of
large numbers of massive BHs embedded in the bulge and disk that result in an inflated
vo and Mbh
value, but this value might still be useful.
KaMbhmw seems
too high too. But, Ghez reports that there are remnants of star clusters
orbiting close to the central BH inside the orbit of S0‑2 that have combined
mass of, perhaps, 105 Mʘ or more. This mass
would add to KaMbhmw
because all orbiting material in the bulge should respond to the 2-D (1/r)
field under the CHUP. Maybe there is a lot more unseen remnant material than
has been recognized so far.
Or else, KaMbhmw really
is this high and we have found the missing mass in central SMBHs, galaxies and
galaxy clusters.
Ghez’s Computation:
We
should be able to duplicate A. Ghez’s calculation of Mbhmw.
With the standard gravitational constant G = 6.67384 x 10-11
m3kg-1s-2 and using the above
observations and Standard Kepler’s 3rd law (K)
KMbhmw
= 4π2r3/GP2 = (4π2/G)(r3/P2)
= 5.915 x 1011m-3kgs2 (1.551
x 1014m)3/(4.98 x 108s)2
= 3.990 x 1038 kg
KMbhmw
= (3.990 x 1038 kg)/1.9891 x
1030kg/Mʘ
= 2.01 x 108Mʘ
This value is a little low, Ghez’s reported
value being 4.3 x 109 Mʘ.
Obtaining r = a, the orbital
semimajor axis, is just simple algebra using the periapse length, Rmin,
and Ghez’s other data including the eccentricity of the orbit of S0-2:
a = Rmin/(1-e). She gives the period, P = 15.78
yrs. We would have to take the values of her data at the extremes of their
error ranges to duplicate her number. But, this still tests the math and we see
that what we have used is correct.
The conclusion is that the Postulate is plausible, at least. The only problem is that the Schwarzchild radius, rs, for such SMBHs, assuming a perfect stationary BH, is rather larger than the observed periapse of S‑2. The virtually infinite spin rate of the SMBH below the event horizon could distort it in a way that precludes even an approximate calculation like Schwarzchild’s resulting in rs << Rmin.
Ultimate
meaning
Therefore, pushing the Postulate to its
ultimate meaning, we find an M - sigma, an AVD and a Keplerian result. It
is actually observed that this putative hyperbolic 1/r gravitational field of
the galactic central SMBH 2-D disk singularity ignores the event horizon and
can reach beyond the galactic periphery. It can reach far far beyond because it
is a 2-D spacetime entity. That is, the Postulate must actually supplant exotic
DM and usurp all its supporting data[70],[71],
including that data sustaining the anomalous velocity dispersion[72],
the Sunyaev‑Zel’dovich[73]
effect, many of the CMB phenomena and galaxy collisions like the Bullet Cluster
effect[74],
etc., as the following remarks reiterate.
Because its accompanying gravitational force
is so much more extensive and more substantively far ranging than an inverse
square G ‑ force, it has a more substantial non-zero effect on other
nearby galaxies which also may have central supermassive black holes with
similar (1/r) gravitational forces in play. This amounts to the existence of a
special “1/r” connection, link or conduit between the central SMBHs in galaxy
clusters. This possibility explains all the phenomena associated with Dark
Matter, including present and primordial large scale structure.
The Postulate does not deny Dark Matter. It
defines it.
Gravitational
Ground State
It is postulated that the HSBH G* field emanates from below the event
horizon where time may run backward, because relative velocities (to us),
exceed c. This may really mean that, among other things, energy relations like
quantum level hierarchies are reversed or upside down. The “gravitational
ground state”, in our normal external parcel of spacetime, is an excited state
if it could be observed from below the event horizon and vice versa. When
in-falling stars “fell” below the event horizon, they began to be elevated in
state as they then “rose” toward the central singularity and enjoyed
dimensional contraction. Relative to us, ironically, the 2-D hyperbolic
gravitational field below the EH may be regarded as an excited state field of
the false vacuum (which is, or at least contains, a huge Black Hole – it may be
a plenum).
The fate of matter in BHs described here removes
a serious criticism of general relativity. The Schwarzchild metric and other
similar solutions to GR imply that matter spinning into a black hole must
undergo a sort of “UV catastrophe”[75]. Its
spin rate below the event horizon must rise to levels wherein it must radiate,
by means of spacetime gravitational waves that are immune to the event horizon[76],
energy equivalent to UV or gamma ray levels and even far above this. And that
would soon cause such matter to “evaporate” by gravitational radiation and escape
the black hole.
We will say that, like Bohr and DeBroglie, this
catastrophe simply does not happen. It does not because all BHs are quantum
objects. They exist in a stationary “state”. A specific permitted mechanism or
process is required to alter this state.
Evaporation by gravitation waves from a
single BH in this particular way is not permitted. If a BH was to transition
from a more excited state[c]
to a lower state, it could emit gravity waves and this would be permitted. If
two BHs were to collide, they would become excited and the combined entity
could transition to a lower state and this would be permitted.
UV Completeness and Gravitational Quantum
Renormalizability
There is no such thing as an ideal[77],[78],
unperturbed, non-rotating, stationary perfectly spherical BH. So, by means of
the HSBHG field postulate, general relativity can be refined and it can be said
to be “UV complete” because 2-D gravity is quantum renormalizable[79] and
quantum events involving 3-D gravity can be transformed to a 2‑D equivalent and
vice versa by means of the
holographic principle[80]. If
the hyperbolic field Postulate is admitted, GR does not need to be refined, at
least not for the reason of UV completeness.
That is, if the whole universe is considered
to be a projection onto a 2‑D surface of, say, a super mega-massive ultra-large
black hole event horizon by appeal to the holographic principle, then all
quantum processes involving gravity may be treated by further appeal to
holographic 2-D + t black hole
quantum mechanics and dynamics. Then,
one may perform the projection or transformation in reverse to get a 3-D + t
result.
Thus, the path to a simpler, empirically
relevant, falsifiable, UV complete, relativistic quantum gravity may be wide
open by this simple singular expedient.
Some
potential implications of the hyperboloid
This massive “flat”, relativistically
plausible, SMBH spacetime spin disk is a hyperboloid of one sheet, not really
truly flat. It has an actual saddle[81]
or an hourglass shape[82],
its being embedded in a 3-D + time universe. The curvature of the hyperboloid
does not become apparent until r becomes very very large, far beyond the galaxy.
So, engaging other galaxies with their own SMBH more intense hyperbolic fields,
the "plane" or surface of this curved sheet will interact with them
more readily simply because of its more complex shape: it is not really “flat”
over vast cosmological distances.
Hyperboloid of one sheet emanating from a virtual point
so that the neck diameter is only one or a few Planck distances.
This proposed cooperative tendency between
galactic hyperbolic (1/r) gravitational fields is one way to account for the
observed large scale network or “cobweb distribution” of galaxies contained among
assemblies of clusters and superclusters. Along with the extended longer range
or more intense (1/r) gravitational force between central galactic black holes,
it also helps account for the theoretically
required primordial structure of the universe, as massive and supermassive
black holes must have been extremely common in the very beginning. They
probably have even formed as massive daughter particles in the decay of the
original inflaton particle[83].
We must remain consistent. If Alan Guth’s
inflation postulate is taken seriously, then his idea of a quantum inflaton
particle must also be entertained. Though the inflaton cannot decay to new
smaller inflatons[84],
it could decay to innumerable black holes as
well as to ordinary “free” matter and energy[85].
Perhaps the radiative particle size would
conform to a Planck distribution because of the involvement of a primordial BH
and the propensity to act as a black body, truly black. As a mechanism of
decay, the inflaton particle may have been a huge black body that began to
radiate BHs, free matter and energy at an enormous rate and temperature while
its 2‑D excited gravitational field began to reorganize or disintegrate into
the nascent ground state 3-D field that we see today. But presently, the
universal 2-D field is still here. Dark
Energy too
The universe may have come into existence as
a probabilistic statistical phenomenon. Guth’s inflaton particle may have
simply emerged from quantum chaos as a virtual particle. Its partner, a virtual
antiparticle, should be out there in metaspace somewhere. Statistical emergence
of
a hyper-excited virtual state is far more
probable than emergence of a lower energy or ground state: the higher the
excited mass-energy, the higher the probability[86].
And, for every fundamental force field there
is a fundamental particle. The Black Hole singularity may be a fundamental
particle corresponding to the hyper-excited 2-D gravitational field.
So, the HSBHG field, when extended to subsume
the whole universe, can account for Dark Energy too. By Figure 1, the
hyperbolic gravitational potential energy profile is generally higher than the
inverse square P.E. profile, when natural units are used and zero (the ordinate
axis) and x = 1 in the diagram are deemed unique.
If the universe can be said to have begun
with an hyper excited 2-D hyperbolic gravitational false vacuum field, its
transition to a 3-D universe with an overall inverse square “ground state”
field may then be a time dependent transition within a quantum-like
superposition. This 2‑D excited potential energy may be spontaneously donated
continuously, over time, to the 3‑D “ground
state” allowing for the Big Bang itself and later, accelerating expansion of
spacetime and the apparent kinematic repulsion of galaxies, clusters and super
clusters. In other words, Fig. 1 says that the BB is not yet done[87],
see ref. 74.
We,
at the present time and place, may be at between 2 < x < 4. We could not
be near x = 1. We may be following a trajectory that is a linear
combination of these two time dependent states, in a quantum-like
superposition. Resumption of acceleration then occurs at the observationally
appropriate time.
Requiring
consequences on the local scale, we observe the ongoing time-dependent quantum
“subsidence” of the 2-D field into the 3-D field by the transition of its
generally higher level of potential energy into the 3‑D spacetime matrix’s
induced “kinematic” expansion energy. As the way a tsunami may engulf a small
island or a ship near shore, the expansion wave would be hitting us right now.
We may thus be seen
to be “surfing” the boundary of the 2-D versus 3-D + time universe as
our little planetary dwellings are swept away in an expanding universe.
The universe we see with our telescopes is
all in the deep past. Only the black curve, before t = the present, is relevant
to observation now. In the future, only the red curve is germane, the black
curve being the final state toward which the red curve is transitioning.
See the reference [88].
The first diagram element at the hyperlink (also
shown below in Fig.1) implies that the 2-D HSBHG field, when extrapolated to t
= 0 to become the initial excited “inflaton” false vacuum field, could be the
“source” of inflation. Interpretation of the whole diagram reveals that it may
also be the source of DE, which begins to have an overwhelming effect, an
accelerating effect, near and beyond about 1/3 to 1/2 of the Hubble time (and
the Hubble distance, interpreted so that our time and distance would be at between
x = 2 to 4). This is roughly what observations imply.
Figure
2
But, it could also indicate the source of the
inflaton particle’s enormous excited state energy. The difference between the
3-D ground state universal gravitational P.E. and the 2-D, HSBHG, excited,
inflaton, false vacuum field P.E. becomes as near to being infinite close to
the ordinate and to the origin as may be necessary to explain its effect.
So, it is really very plausible that what
triggered inflation was random statistical variation, like radioactive decay,
applying to an ensemble or multiverse of inflaton particles in an excited false
vacuum field. This fits in with both DM and DE according to the Postulate.
Inflation and the inflaton field, with their
implied “Many Worlds”[89]
interpretation, are thus not unfalsifiable. The hyperbolic gravitational field
provides us a handle on this. The overall parsimony of the Postulate is
remarkable.
Many
Worlds
also allows for the existence of virtual antiparticles of the numerous extant inflatons.
They would be called anti-inflatons and would be composed of antimatter. “Dark
Flow”[90]
might be due to our close proximity to an antimatter twin. We may be in for a
“Big Crash”. Allowing that the universe was quantum in nature to begin with and
that it is still a quantum entity solves even more problems than we might have
thought.
Newton’s
law of gravitation
Newton’s law of universal gravitation[91]
will accommodate a 1/r gravitational field only if spacetime is not limited to 3
dimensions plus time, by appeal to general relativity[d].
Kepler’s laws can be modified to accommodate a (1/r) field because these laws
assume Newton’s[e], and
Newton’s law needs only to be rewritten for hyperbolic, gravitational, (1/r)
2-D spacetime by replacing 1/r2
with 1/r. Similar
substitutions will adapt Kepler’s laws. One must always remember to include r*, the unit vector of r, in such substitutions to
account for dimensional requirements. The HSBHG 2-D spacetime parcel possesses
mass and gravity within an excited state, like the highly excited inflaton
field of the false vacuum postulated by Alan Guth[92].
The special inter-BH 2-D (1/r) gravitational
connection between galactic central SMBHs may constitute a sort of skeleton or
scaffold upon which is hung all the other matter in the universe. So, the large
scale structure of the universe is also taken into account. The primordial
large scale structure would have arisen from those swarms of black holes that
could have been produced when the inflaton initially began to decay.
Some
Issues
The concept of a
potential that falls off as 1/r raises some issues as to the gravitational
potential which would be logarithmic. Might we propose to introduce a cutoff
scale that would limit the effect of the 1/r force over a given distance?
The gravitational potential energy of the
hyperbolic G* field does indeed fall off as ln(x), but this is good. If the
inverse square, G field P.E. diagram and the hyperbolic G* field P.E. are formulated in equivalent ways (Fig. 1, in natural
units with the x = r values of 1 and 0 having special significance), then the
P.E. diagrams are superimposable (but certainly not congruent)[93].
The hyperbolic field would be effective only in
the plane of the SMBH and the spiral galaxy’s rotation and in the bulge so,
this is a sort of cutoff. It is more long range than the inverse square field,
it is true. But this is good too. The last thing we want to do is cut this off
further. So, no artificial cutoffs are necessary, other than the intuitively
natural one that is used to superpose the inverse square’s hyperbolic P.E.
diagram upon the (1/r) derived one, the ln(x) curve.
Inside a galaxy,
standard Newton and Kepler still hold. And, the central SMBH is nominally only
a tiny fraction of the mass of the whole galaxy, unless the Postulate shows us
otherwise, that is. So, its overall effect might not be dominant[f] and the hyperbolic G* force falls off to a
small constant limiting value of ao,
as suggested by Milgrom[94].
The hyperbolic field
induces a parametric constant G* force dependent only on Mbh and G* independent of distance
r. The resulting small constant velocity stems from a constant radial
rotational acceleration (not angular acceleration) which Milgrom calls “ao”. He tacks this
onto Newton’s law as a phenomenological necessity. He offers no derivation. The
Postulate suggests a derivation.
This constant stellar
velocity somewhat nearer the galactic periphery, vo is an ideal of course. Other factors may
influence a non-varying peripheral stellar vo,
like the probable presence of numerous other
large BHs embedded in all galaxies.
Conclusion and some speculation
The hyperbolic
supermassive black hole gravitational field is a parsimonious explanation of nearly
all aspects of Dark Matter and Dark Energy. This is not unreasonable because
they say that general relativity must break down at a black hole singularity.
This means that the physics of singularities is unknown. Appeal to quantum
gravity is only conjecture. So, nobody can say for sure what may or may not be
possible[g].
The HSBHG field also saves GR from the very flaw
or limitation that the indication of singularities is claimed to induce. The
postulate says that Birkhoff’s theorem and other views of GR singularities cannot
be relevant. Even the Kerr metric is unrealistically simplistic. No real black
hole has anything like the naive properties that are supposed for it. All
genuine black holes must spin very rapidly, especially beneath the event
horizon (where they might spin or rotate backward or have no observable
rotation because of the time dilation or the time reversal effect of
orbital/rotational velocities that exceed c). All real black holes have event
horizons that must be massively distorted and perturbed as a consequence of a
singularity with a virtually infinite spin rate, especially supermassive black
holes near galactic centers. This fact must have consequences
The postulate says that the “virtually” infinite
rotation rate at the Heisenberg delimited singularity induces a sort of phase
change in spacetime. A dimension is spun out, eliminated from the set. And, the
flat 2-D singularity is still subject to some version of CHUP. Hence, it can be
said to remain only “virtually” infinitely dense, being only a “virtual” 2‑D planar
mass.
Black holes are certainly not ordinary
gravitational objects[h].
This is a sort of quantum gravity because only
2-D spacetime can sustain a hyperbolic gravitational field. This 2‑D gravity
field is quantum renormalizable[95]. The holographic principle can then be invoked
to solve any problem in quantum general relativity (QGR) for a 3-D + time
universe by solving in 2-D and projecting in reverse from the 2‑D back to the 3‑D
case.
The HSBHG field may well be a theoretical basis
for the M-Sigma relation. Hence, it need not follow the empirical relations got
by other workers. It may help explain the observed anomalies in the relation, especially
those that involve central supermassive black holes of over 109
solar masses. Certain other anomalies may be tied to the HSBHG field.
The Postulate is an unusually parsimonious
way to reconcile observations without introducing new exotic subatomic
particles or tinkering with Newton (or with Einstein, for that matter). Experimentally,
a negative result for the Postulate would be just as interesting as a positive
result. There may be other ways that we might be able to deduce what is happening
under the event horizon and near the singularity besides just automatically claiming
superiority of a mere conjecture like quantum gravity[96].
If quantum gravity hypotheses can be admitted, then this Postulate can be
entertained.
There other anomalous phenomena that may be
explained by the Postulate. For instance, the anomalous orbital behavior of the
moon might be another of its effects[97].
This would help confirm that there may be an extended form of SMBH
gravitational frame dragging that distorts the moon’s orbit over time. Then the
orbits of other moons in the solar system may show similar effects.
By the way, we see now that virtually all
longer range more intense gravitation on cosmological scales might be
dominantly 2-D hyperbolic in nature. This is a rather incredible statement to
make.
But, what if it’s true?
Bibliography
Upon print publication, this bibliography
will be made available online at the aforementioned blog entry74 so
that references may be followed more easily.
[a] Milky Way Mass, Mmw = 7×1011 M☉ Reid, M. J. et al. (2009).
"Trigonometric parallaxes of massive star-forming regions. VI. Galactic
structure, fundamental parameters, and noncircular motions". The Astrophysical Journal 700: 137–148, solar mass M☉
= 1.9891 × 1030 kg, so Mmw = 1.4
x 1042 kg
[b] Milky Way Mass including “Dark Matter”
1–1.5 × 1012 M☉
McMillan, P. J. (July 2011). "Mass models of the Milky Way".
Monthly Notices of the Royal Astronomical Society 414 (3): 2446–2457. solar mass M☉
= 1.9891×1030 kg so, Mmw = 2 x 1042
kg, with DM
[c] A BH must exist in an exited state because,
below the EH, all energy relations and time are reversed.
[d] GR permits a hyperbolic G*-field if spacetime
is limited to 2-D – see reference 9 of the endnotes.
[e] Kepler’s laws to be rewritten for the 2-D
case simply by substituting rr*
for r2, since
Newton’s law for the 2-D case is also got this way.
[f] It turns out that it is dominant. Our
calculations here show that the central supermassive BH may rival the mass of a
galaxy. With a better value of G* for the G* field, it may account for 100% of Dark Matter.
[g] It is said that GR and all other physical
laws must break down near the infinitely tight spacetime curvatures of BH
singularities. Still, an effort should be made to state what is possible and
what is impossible therein. But, unfalsifiable, purely hypothetical theoretical
systems cannot be invoked to put a kibosh on Einstein’s, Kerr’s, Schwarzchild’s
and Kretschmann’s analyses of BH singular infinities.
[h] The goal of science should be to simplify.
All that need be done is admit that BHs are unique and implied infinities or
singularities must be seen through cosmological Heisenberg’s tinted glasses.
This may be all the quantum gravity that we need. Besides, who says we need a
Theory of Everything (TOE) or a Grand Unified Theory (GUT)? Why cannot there be
a two sided coin, a Grand Duality? The Great Tao of Physics (GTOP) would be
pronounced “GEE top” and sounds just as cool. Would this not be better in terms
of the favorite Eastern philosophies of many physicists?
[61] Ref. (43)
[64] http://members.fcac.org/~sol/chview/chv5.htm The Stars of the Milky Way
[65] 68–95–99.7
rule Normal distribution http://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule
[66] arXiv:1005.0385v2 20jl2010
Our milky way as a
pure-disk galaxy – a challenge for galaxy formation, Juntai Shen, R. Michael Rich, John Kormendy,
Christian D. Howard, Roberto De Propris, Andrea Kunder
[67] http://en.wikipedia.org/wiki/M-sigma_relation, An original diagram of the M-sigma relation
by the article’s author
[68] Ref. (30) Ghez
[69] Rs = 19.1 parsecs for a 200 billion
solar mass black hole – versus implication of Rs £ ≈ 0.5 parsec according to Ghez. This much
larger BH event horizon is predicted from the Postulate. It could explain why
bulge stars are all subject to the hyperbolic (1/r) gravitational field. Their
orbits all must cross the galactic plane and intersect the hyperbolic field
whence they would be under the influence, however briefly, of the hyperbolic
field. They are not sucked in because they possess (1/r2) inertia
and the distance traversed is small.
[71] Evidence for Dark Matter
[72] http://arxiv.org/abs/1204.0144 Raphael Sadoun, Jacques Colin, Purely phenomenological M-sigma, AVD
correlation, claiming an implied Dark Matter connection to M-sigma
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New results from new constraints and improved strong lensing modeling
technique, http://arxiv.org/abs/1209.0384
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Claude;
Diu, Bernard; Laloë, Franck (1977). Quantum Mechanics: Volume One.
Hermann, Paris. UV catastrophe
[76] Guth, Alan H. The Inflationary Universe, 1997, Perseus
Books, Gravitational waves are immune to
the event horizon, as ripples in spacetime and, just the same way, spacetime
itself may exceed c, like it did in the first instant of the inflationary
BB.
[77] Misner, Charles W., Kip S. Thorne, John
Archibald Wheeler (1973). Gravitation. W. H. Freeman. pp. 875-876. Hairless
black holes
[78] Greene, Brian (2010). The Elegant
Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate
Theory, 2nd Ed.. USA: W. W. Norton & Company, page 321.
[81] Shapes of the universe http://imagine.gsfc.nasa.gov/docs/features/exhibit/map_shape.html
[82] Hyperboloid shapes http://www.thefreedictionary.com/Hyperboloid+of+one+sheet
[83] http://arxiv.org/pdf/1107.3003.pdf Daughter particle of
the original inflaton particle, a super mega ultra-massive BH
[84] http://prd.aps.org/abstract/PRD/v69/i7/e075012 Inflaton particle cannot decay to new smaller
inflatons
[85] D. Boyanovsky, H. J. de Vega, N. G. Sanchez Particle decay during inflation: self-decay of inflaton
quantum fluctuations during slow roll, http://arxiv.org/abs/astro-ph/0409406
[86] Guth, Alan Inflationary universe: A possible solution to
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[90] NASA/Goddard
Space Flight Center (2010, March 11). Mysterious cosmic 'dark flow' tracked
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[91] Proposition 75, Theorem 35: p.956 - I. Bernard
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[92] Ref. (26)
Alan Guth
[93] Ref. (26)
Alan Guth
[95] Quantum renormalizability of the 2D
gravitational field http://arxiv.org/pdf/gr-qc/9605004v1.pdf
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