Black-Hole Gravitational Field

The Hyperbolic

Black-Hole Field Anomaly

Supermassive black-holes pervade the universe. In the field of our view, within the light cone of our observational limit, there are over 200 billion supermassive black holes residing at the centers of large galaxies. There are probably many more large naked black holes residing in enormous dust clouds or simply standing alone as bald singularities in elliptical galaxies and globular clusters and within galactic clusters and superclusters. These invisible black-holes simply have not had enough time to accumulate a large cloak of glowing matter that emits light by virtue of its in-fall to their event horizons. Therefore, they are truly black.

Black-holes and their hyperbolic gravitational fields fully account for the dark matter necessary to keep galaxies spinning at their observed rates and to bind galactic clusters and superclusters. If there are large enough numbers of such black holes to do this job, then the assumption of the Cosmological Principle is dead wrong by this fact alone.

It is as though the universe is made of Swiss cheese and we have assumed it is made of white cheddar. It is well known that a medium filled with small bubbles or tiny solid particles behaves very differently toward the propagation of any type of energy through it. Numerous small bubbles, for instance, lower the speed of sound and affect the way a medium like water absorbs microwaves. Shock waves propagate so differently that the behavior of the explosion front in the conventional chemical explosive has to be taken into account in the design of nuclear weapons. Bubbles and dispersed solids must be avoided.

When assumptions are made regarding the type of "perfect fluid" of which the universe is made we cannot disregard exceptional circumstances like the presence of a froth of black-holes embedded within it. It matters little that there are good reasons for using approximations like the Cosmological Principle. Something must be done to allow the formulation of comprehensible theory giving the means for tractable calculation. But, this theory and such calculation must be regarded as only approximate. Unless steps are taken to greatly refine theory and bring calculations up to a much higher standard, there shall be no such thing as "precision cosmology".

The hyperbolic black-hole (HBH) gravitational fields, stemming from supermassive black-holes at the centers of galaxies, extend far beyond the visible boundaries of the galaxies themselves. The Modified Newtonian Dynamics (MOND) effect shows that these fields may be virtually infinite in extent. If this is so, the spacetime continuum that is actually present in the universe is very different from the one that Einstein assumed. These oversimplifications are implicit in the Friedmann LeMaitre Robertson Walker metric that Friedmann used to formulate the form of the General Relativity equations that cosmologists commonly use. In other words, the whole structure upon which is built the argument for acceleration of the rate of expansion of the universe and the existence of dark energy (not to mention dark matter) is deeply suspect.

It is just too bad, so sad, that so many physicists have devoted whole careers to mastering the mathematics of General Relativity from the perspective of the FLRW metric and the Friedmann equations. These anachronistic personalities will simply have to die off or retire before we can make progress. After all, there is some truth in the saying about physicists who see everything in terms of some simplifying assumption. "First, we assume a perfect sphere." is not how to do critical science deserving of massive funding.

Only spacetime itself is homogeneous and isotropic. But, once it becomes filled with supermassive black-holes and other dark naked singularities, it cannot be treated this way with any degree of precision or accuracy. Some investigators have already picked up on this fact. They are formulating new cosmologies with different metrics and are abandoning the oversimplified assumptions that were designed to make calculations easy. Much too easy. They have come to appreciate the power of supercomputers and advanced mathematical logic programs to handle more realistic models of the universe. This twenty-first century trend is only just beginning. The real revolution in cosmology has yet to come. It will be a counterrevolution, for the twentieth century is dead.
　
　
　

Modified Newtonian Dynamics

MODIFIED NEWTONIAN DYNAMICS AND THE BLACK-HOLE HYPERBOLIC GRAVITATIONAL FIELD

Albert Einstein easily derived and wrote a relativistic differential equation that was guaranteed to reproduce Newton's Law of Gravity when it was integrated. He could have just as easily written a differential equation that reproduced MOND, but he didn't. He just didn't. He had no reason to do so since the various MOND observations had not been made. So, let no-one say that MOND contravenes relativity.

So, relativistically speaking, if we consider the definition of a black-hole, it must be accompanied by a very characteristic and very different gravitational field. Because it is a singularity, a single point-mass with infinite density (at the limit as the center is approached), it must possess a gravitational field that is defined and determined by its single point, its singular property. Its gravitational field must therefore approach an asymptote at radius = 0 and, and by symmetry, it must approach another asymptote at radius = infinity. This is the definition of a hyperbolic field, NOT one that follows Newton's inverse square law, which is parabolic.

If black-holes posses hyperbolic gravitational fields, then there is no mystery in MOND. No big deal. Look at this image of a whiteboard derivation of the hyperbolic black-hole (HBH) gravitational acceleration and velocity profile near a galaxy containing a supermassive black-hole at its center. On the whiteboard, I also have written a synopsis of the MOND development.

NOTE: In the HBH segment, r must be multiplied by k. Here, k = 1m (S.I.) for dimensional integrity. In other words, F = GMm/kr, k = 1m (S.I.) all the extensions of F have the same caveat.

GO TO

HTTP://WWW.LONETREE-PICTURES.NET/

AND PRESS THE MOND BUTTON TO VIEW A BETTER VERSION OF THIS IMAGE.

Use the backarrow button <<--- to return here or else

you might close out of NEO-COSMOS

Of course, something must be done to compensate for the fact that (GM)^1/2 does not have the dimensions of a velocity, G x M not being divided by r. This could be resolved with the adjustable parameter ratio b/d having a dimension the same as 1/r. OR, better yet, multiply r by the absolute value of the unit vector of r, retaining the unit. This would be a mathematical acknowledgement that we are dealing with a singularity.

For MOND, Newtonian gravitational acceleration is denoted aN. The variant acceleration due to MOND expresses aN in terms of an acceleration that is modified by the function μ(a/a0), which is equal to 1 when the radius from the center is small enough for the overall gravitational acceleration to be large relative to the MOND constant, a0. When the putative acceleration is small relative to a0, μ is equal to a0 such that the equations on the lower left are satisfied. This happens when radius r is large enough for a2/a0 = aN = GM/r, and the total force of gravitational attraction enters the MOND regime. These values for r are equal to and beyond the point where the velocity distribution of stars encircling the galaxy in its outer regions becomes constant.

Remember, M = the mass of an entire galaxy with its black hole. M2 = the supermassive black-hole mass while M1 = mass of the stars in the disk inside the radius r, to a given star. This radius might enclose more than 95% of all the stars in the disk and so may as well be considered to enclose all of them. But, a graphical model would have to take a sliding percent enclosure into account in order to plot a theoretical velocity distribution. So, it will be a little while before I actually do this. Maybe I’ll just assume a Gaussian distribution for the number of stars with a given average velocity in the disc and a different Gaussian for the stars in the spheroidal bulge. The bulge must be chaotic and so it would follow different statistics. This is why the net velocity fades to zero in the bulge.

According to Newton’s inverse square law, velocity should fall off rapidly toward zero in this outer zone as the periphery is approached. But, observations show that it does not. Instead, it falls off much more slowly and becomes constant according to the vMOND equation on the lower right.

But, the hyperbolic field contribution to the overall galactic gravitational field shown as the blue curve, y2, in the graph above, gives precisely the same result. Thus, vMOND = vHBH. If it is admitted that black-holes are different, that they have special properties, among them that they are gravitational singularities, then this is not too surprising. In fact, it should have been thought of before, and it probably has. But, it is now being overlooked. I hope this effort on my part may prevent this oversight from being propagated indefinitely. Sorry, there will never be a Nobel for MOND.

Note that the usual depiction of the velocity profile of a spiral galaxy shows velocities rising to a maximum as one moves toward the center whereupon they fall off virtually to zero as one gets very close to r = 0. My simpler velocity distribution profile is for just one or for a very few stars. The standard picture of a maximum and fall-off in velocity occurs because stars get crowded approaching the center and their orbital paths become chaotic. As one moves closer in, just as many stars move clockwise as move counterclockwise (and on more nearly perpendicular trajectories relative to the galactic plane) and the net velocity declines. The stellar distribution becomes more spheroidal too, resulting in the classic galactic “bulge”. When I formulate my model, I will have to take all this into account as well. This is going to be fun.

It is interesting to imagine what a galaxy would look like if purely Newtonian F = ma = GMm/r2 ≠ GMm/r for large r. Then, v∞ ≠ (GM)^1/2 = constant. Instead, rotational velocity would rapidly fall off toward zero as r increases without bound. The stars would lag much further and further behind and the spiral arms would wrap around the center much more tightly, like the mainspring of an old wind-up clock. So, one can actually see the MOND effect by just looking.

This means that there may well be no such thing as dark matter or twin matter or any such Baroque complications festooning the simple picture of the universe that we, as scientists, should be looking for. It is in the nature of human beings to overdo. Dark matter and MOND are in danger of becoming vastly overdone.

So, now let me engage in a little bit of my own overdoing.

If this version of MOND is correct, there will never be a measurement of a0 obtained in the laboratory in a supersensitive Cavendish experiment. That is, not unless we can produce some sufficiently long-lived black-holes in the lab. Nor will evidence be found inside or just outside the solar system. HBH MOND requires participation of a black-hole. This prediction will never go over very well with a lot of important people, so it will not be readily accepted.

In elliptical and globular galaxies wherein the MOND effect may be observed, HBH MOND will require that one or more supermassive black-holes shall be found, naked black-holes at that. The intragalactic black-hole presence in galactic clusters and superclusters may not be enough to account for MOND in these objects either, so some naked black holes may well be found to be embedded within them too. Nobody is looking for them now, so it is not surprising that they have not yet been found.

The hyperbolic field concept can be extended to the entire universe, too. If it can be verified, it may go a long way toward an accounting for the mistaken interpretations of acceleration and dark energy in the universe. This would require that the primordial black-hole, the mother of all black-holes or MOAB, must have persisted in some form, probably greatly diminished, for a long time after it started to decay into the universe that we see now. In other words, the highly excited inflaton particle may have taken some time to deconvolve, decompose and collapse, so it may even still persist today, along with its hyperbolic field in which we may still be embedded.

But, if the inflaton paticle decayed and its hyperbolic gravitational field collapsed with it, a transitional Newtonian field rose up to replace it almost instantly. These would be other cases where entities expanded or contracted at many times the speed of light. In other words, the inflation process had reflections or reverberations that we still see today. The old hyperbolic field is not finished collapsing. The new Newtonian field is not finished rising. This would have subtle relativistic effects in their own right.

Let’s just hitch a ride on a really fast space-ship heading on a straight line for deep space in any direction with a destination rather more than 13.72 billion light years away and we just may be able to find out. But, it will take us considerably more than 13.72 billion years. More than 27.44 billions years. Still, surely by then, the MOAB hyperbolic field will have completely dissipated with little or no residual effects.

The good news is, if strange, weird science is needed to justify grant funding, this is it.

INEXPLICABLE REVISIONISM

Some of Our Best Scientists

Have Shown Genius Level Negative IQs

Recently there has been an inexplicable reversal in the usual recitation of facts that scientists have been giving regarding the evidence for dark energy. Here is a quote from a current article on dark energy and dark matter that appears on a NASA website: "Then came 1998 and the Hubble Space Telescope (HST) observations of very distant supernovae that showed that, a long time ago, the Universe was actually expanding more slowly than it is today."

This is grossly untrue. If this is what Saul Perlmutter and Adam Riess have been saying, it is a gross distortion. In them, I am disappointed almost to tears. But, what else can I expect from the antigeniuses among us?

I have been tracking measurements of the Hubble constant for many years. The Hubble Space Telescope has measured H0 for the deep space SNe 1a as the highest yet recorded except for H0 determined for the cosmic microwave background radiation, which is even more "distant" and even older. As one plots H0 measurements against the average distances from Earth to the midpoints of the ranges of objects used in the observations, one obtains a very precise straight line in this scatter diagram. This linear regression line has a very high correlation coefficient (0.98) and a NEGATIVE slope stretching from the origin at t = 0 to now at t = 1.

Given that H0 is not really a constant, older accepted data along with current measurements of H0 show that H0 for very distant and old objects is larger than for nearer and younger objects. Nowhere in any of the peer reviewed publications of Perlmutter nor Riess is there explicit argument for acceleration or dark energy that does not subtly assume what it purports to prove. They never explain exactly how the reversal of common sense occurs that says the universe expansion rate is accelerating in the present era. They do not even acknowledge the reversal.

Commonly accepted facts have to be rewritten to accommodate this circular conclusion. History has to be revised. Accepted data clearly show that the expansion rate is decelerating. See http://www.lonetree-pictures.net/Graphical%20Model%20of%20the%20Universe.htm .

There is lots of evidence against dark energy. Recent papers casting doubt on the Cosmological Principle should be taken seriously. If we should be prepared to accept the many patches and ad hoc band-aids that dark energy requires, why can we not entertain some patches to explain away the so called "evidence" for it and help save the Scientific Method?

One does not validate a scientific principle by accumulating circumstantial evidence. Such are just anecdotes. One must formulate an antithesis; an opposite or negative hypothesis, and attempt to perform a critical or crucial experiment that would confirm or deny it. If this “null hypothesis” is confirmed, the original hypothesis is falsified or nullified. Dark energy is incapable of falsification and is thus as ineligible as a scientific hypothesis as Santa Claus or God Himself. To hold otherwise is to open the gate to superstition.