Monday, March 10, 2014

Spinning Supermassive Black Holes and Galactic Gravitation, Part 2

see the related blog  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 mkg‑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,

vσ  =  “σ”  =  103 km/s  =  103,000 m/s

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 mkg‑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.

See footnotes. [a], [b]

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

   =  (3.0857 x 1013 m/mpc)(0.570 mpc)[69]/1 – 0.8866)

   =  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.

Figure 1

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

click to enlarge

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?



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)
[62]      Eric Christian; Samar Safi-Harb "How large is the Milky Way?". NASA: Ask an Astrophysicist
[63]      Ref. (26)

[64]  The Stars of the Milky Way

[65]     68–95–99.7 rule      Normal distribution
[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],  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.
[72]  Raphael Sadoun, Jacques Colin,    Purely phenomenological M-sigma, AVD correlation, claiming an implied Dark Matter connection to M-sigma
[73]  Sunyaev-Zel’dovich Effect

[74]    J. Richard, A. Morandi, M. Limousin, E. Jullo,D. Paraficz, J.P. Kneib, The Bullet Cluster revisited: New results from new constraints and improved strong lensing modeling technique, 

[75]     Cohen-Tannoudji, 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.
[79]    Quantum renormalizable 2-D gravity
[80]    Holographic principle
[81]     Shapes of the universe
[82]    Hyperboloid shapes
[83] Daughter particle of the original inflaton particle, a super mega ultra-massive BH
[84]  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,
[86]     Guth, Alan   Inflationary universe: A possible solution to the horizon and flatness problems, Phys Rev D, 23/2, 15 January 1981     The statistical emergence of the inflaton  
[90]     NASA/Goddard Space Flight Center (2010, March 11). Mysterious cosmic 'dark flow' tracked deeper into universe. ScienceDaily,  
[91]    Proposition 75, Theorem 35: p.956 - I. Bernard Cohen and Anne Whitman, translators: Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy.
[92]     Ref. (26)  Alan Guth   
[93]     Ref. (26)  Alan Guth
[94]       Mordehai Milgrom, MOND
[95]    Quantum renormalizability of the 2D gravitational field

[96]     Weinstein, Steven and Rickles, Dean,  Quantum Gravity

Dec 26, 2005; substantive revision Feb 23, 2011

[97]      Lorenzo Iorio, On the anomalous secular increase of the eccentricity of the orbit of the Moon,


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