**A Different Theory of Dark Matter-Energy**

The fact that stars and planetary systems in our galaxy seem to be travelling at velocities higher than can be presently explained by the observed mass in the Milky way and other galaxies has led to the prevailing theory that there is some kind of “Dark Matter” which has not or cannot be observed by our present detection devices. In fact, it is thought that this “Dark Matter” is more than 90% of the mass in our universe. Scientists have also determined that there must have been much more mass than is presently observed in the early universe in order for the present galaxies

to have formed.

In addition, the fact that galaxies are presently accelerating away from each other has had a similar explanation in that there must be some “Dark Energy” which again has not or cannot be observed by our present detection devices.

There are two unstated assumptions here. The first assumption is that only mass can generate a gravitational force. The second assumption is that this additional gravitational force is evenly distributed in three dimensional space as is the case with normal gravitational forces or in Einstein terms, space is distorted uniformly around any mass.

What if space can be distorted (or gravity generated) by concentrated energy, such as that contained by a rotating body and that this gravitational force is not uniformly distributed in three dimensional space. This raises the possibility that much less mass or energy is required to explain the phenomena of stars travelling too fast around the center of the galaxies. It is interesting to note that the physical structure of galaxies appears to be uniformly organized in a pancake formation. It is only at the center of the galaxies does there appear to be a spherical bulge.

I would like to offer a different hypothesis to dark matter and dark energy. This hypothesis suggests that what we are trying to explain as some unseen or unseeable matter or energy is in reality no more than the gravitational effects generated by mass moving through space, and in particular when it is confined into a circular motion. Very similar to how magnetism is generated by the motion of electrons when confined to an electro-magnet.

The recent discovery of a galaxy that does not seem to have a black hole at its center also does not show any evidence for dark matter (galaxy NGC 1052-DF2). The star systems rotate at a velocity consistent with the makeup of the galaxy being of normal matter. I believe this further supports my hypothesis.

This discussion is not an attempt to derive a definitive proof of my hypothesis, but to show there is sufficient plausibility to warrant further study. In this light the following are some of the assumptions that I will be using:

I would also like to suggest that there is an engine in the universe that can convert mass into the kinetic energy that we presently see in our expanding and accelerating universe. If we want to know the mass of the universe in the distant past we need to take into account the kinetic energy of this expanding universe. Although I cannot give a good scientific reason, I would like to suggest that this engine is the high rotational velocity of massive black holes. And this repulsive force emanates from the axial ends of these rotating black holes.

- The kinetic energy of a rotating mass can curve space and time and thus generate what seems to be a gravitational force.
- This effect is only noticeable at masses similar to black holes and rotational velocities approaching the speed of light.
- There is insufficient kinetic energy even in our sun to generate a measureable effect on objects within the solar system.
- This curving of space and time is non-uniform.
- At the equator the curvature is such that mass in its vicinity will tend to move toward it.
- At the ends of the rotating axis the curvature is such that mass will move away from it.
- This force varies with the inverse of the distance from the rotating object rather than with the inverse of the square of the distance as is the case with the normal Newtonian gravitational force.

**Explanation of why Rotational gravitational force varies in a different manner with its distance from its source than normal Newtonian Gravity**

The following thought process is used to explain why rotational gravity might vary with 1/r instead of 1/r^2.

Let us start with Newton’s gravitational equation (it would be more accurate to use Kepler’s formula, but for the sake of simplicity I will use Newton’s equation).

I will rewrite his formula as follows:

F = G*M*m*4π/A (I am assuming that M is much larger than m)

I have replaced r^2 with the surface area of a sphere emanating from the center of the mass in question. This suggests that gravity varies with the geometry of the space surrounding this mass. The reason for this will be seen later.

Next I want to rewrite Newton’s equation in the form of energy as opposed to just mass. This will allow the inclusion of gravitational forces from other sources than just mass.

Thus:

F = G*E/c^2*m*4π/A (I have replaced M with E/c^2 as per E=M*c^2)

Here I am assuming equivalence between mass and energy.

This now allows me to consider other forms of energy such as Kinetic or rotational energy. In most cases the other forms of energy are so small compared to that contained in mass that they have a negligible gravitational effect.

However, I suggest that at the mass and rotational speeds of black holes the gravitational effect can become significant.

I will now rewrite Newton’s formula considering the Kinetic energy of a rotating black hole.

F = G*KE/c^2*m*4π/A

where KE is the kinetic or inertial energy of the rotating black hole.

Although the gravitational force for a mass emanates uniformly from its center and thus varies with 1/r^2, this would not be expected to be the case for rotational gravity. Gravity from a rotating body might be expected to emanate along the axis of the rotating body and would not be uniform throughout space, but along lines perpendicular to axis of the rotating body.

Thus the area extending out would be 2πrD.

Where r is the distance out from the axis of the rotating body and D would be the diameter of same.

We can now rewrite Newton’s equation as follows:

F = G*KE/c^2*m*4π/(2*π*r*D)

or = G*KE/c^2*m*2/(r*D)

Based on this we can see that this rotational gravitational force would vary with 1/r instead of 1/r^2. This gravitational force would only be effective in a pancake type of system and any object outside of this pancake area would not be affected by this force.

Should there be an observation of a body rotating at too high a speed outside the axis of rotation of the Black Hole would immediately refute my argument for rotational gravity.

- The formula for this rotational gravitational force is presumed to be:

F_{ai} = G*KE/c^2*m*2/(r*D)

Where:

F_{ai} = Attractive rotational force

G = Newton’s gravitational constant

KE = kinetic or inertial energy

c = velocity of light

D = Length of rotating mass along its axis of rotation

r = Distance of another mass (star system) from the central core.

m = mass of distant object (star system).

KE is assumed to be (1/5*M V^{2}) = kinetic energy of the rotating mass (this is the kinetic energy of a solid rotating sphere). This may or may not be the case as no one knows what the internal properties of a black hole are. For this case I shall assume that it exhibits the properties of a solid rotating sphere.

9. For simplicity’s sake I’ve chosen to use the Newtonian formula for gravitation force as opposed to Kepler’s more accurate description of planetary motion.

*Two groups—in Germany and the U.S.—monitored the orbits of individual stars very near to the black hole and used **Kepler’s laws** to infer the enclosed mass. The German group found a mass of 4.31 ± 0.38 million **solar masses*^{[2]}* while the American group found 4.1 ± 0.6 million **solar masses**.*^{[3]}* Given that this mass is confined inside a 44 million km diameter sphere, this yields a density ten times higher than previous estimates. A more recent study suggests that this mass is closer to 1 million solar masses*

*Measured velocities of stars close to the center of our galaxy ranged from 0.5% to 2% of that of light. More recent estimates suggest that the rotational speed is 1.67% the speed of light or 5×10^6 meters per second.*

There are still large amounts of additional mass that is in close proximity to the central extremely dense mass (black hole) and contributes to additional gravitational forces on the orbiting stars in the solar system.

Using these assumptions it is believed to be possible to explain the phenomena presently being credited to dark matter.

**Calculating the point at which the Newtonian gravitational force equals the rotational gravitational forces in the Milky Way galaxy.**

In other words at what point does this proposed rotational gravitational force be equal to that of the normal Newtonian gravitational force?

This would occur where:

F_{ai} = G*KE/c^2*m*2/(r*D)

G*M_{1} *m/ r^{2} = (G*.2M*V^2)/c^{2}*m*2/(r*D)

Newtonian Rotational

This becomes

M_{1} / r = (.2M*V^2)/c^{2}*2/D

1/r = .4*M*V^2/(c^2*D*M_{1})

r = (c^2*D* M_{1})/(.4M*V^2)

Where:

G = gravitational constant.

M_{1 } = total mass close to the center of the galaxy which includes both the rotating black hole as well as other mass close in which is not part of the black hole. For the Milky Way the total mass close in is approximately 1000 times greater than that of the rotating black hole. Thus M_{1} /M = 1000

This becomes

r = 1.58__x10__^{18 }__meters = 167 light years__

**It is interesting to note that the curve depicting the velocity of star systems rotational velocity around the Milky Way flattens at very close to this distance from the center of the Galaxy. See graph later in this presentation.**

This would explain why the rotational velocity of planetary systems becomes flat after a certain distance from the center of the galaxy due to the fact that the rotational gravitation force is proportional to one over the distance or 1/r instead of 1/ r^{2} .

**Would we see any effect of rotational gravity within our solar system?**

If the above is true what would be the rotational gravitational effect of the sun be on the planets in the solar system. Where do these two forces equal each other for our solar system? Assume that the rotation of the sun provides the rotational gravitational force.

Again

r_{o} = (c^{2}*D)/(.1* V_{s}^{ 2})

D = 1.39E9 meters

V_{s } = rotational velocity of sun 1870 m/s

r_{o} = 3.58×10^{20} meters or 37800 light years.

This is obviously well outside the solar system and thus the rotational forces due to the rotation of the sun would have no impact on any of the solar system’s planetary bodies.

**Predicting the velocity of the solar system based on the preceding theory:**

One way to test this hypothesis is to see how well it would predict the velocity of the solar system around the Milky Way.

Assuming that the bulk of the gravitational force on the solar system is due to the rotational gravitational force we can express it as follows:

G/(c^{2} *2*D)*(.2*M V^{2})*m /r = m*v^{2} /r

Rotational gravity force centripetal force

m = mass of solar system

v = velocity of solar system around the galaxy

V = rotational velocity of central mass (Black Hole)

We can see that m and r will cancel out and transposing we get:

v =( G/(c^{2} *2*D))*(.2*M V^{2}))^.5

I’ve assumed M to = 1 million solar masses and

V = 1.67% of the speed of light

D = 44,000,000,000 meters

Therefore:

v = 290,000 m/s

The actual velocity is 222,000 m/s

This is remarkably good accuracy considering that the mass, diameter and rotational velocity of the central (black hole) is not accurately known. In addition we do not know what the physical structure of the black hole is and thus we do not know its actual inertial energy.

**The question we can now ask is what happens at the ends of this rotating mass. Are there any gravitational effects parallel to this rotating axis?**

I do not have any good basis for the following assumption that I am going to make, however I do wish to explore the possibility that this rotating black hole might also account for our expanding universe. Thus I make this purely speculative assumption that there is a negative gravitational force emanating from the ends of this rotating mass. I will also assume that the equation for it is the same as I have developed in the perpendicular direction from the rotating axis, but is negative in force.

In order for this postulation to work there would have to be a large source of energy input. The only way I can see this happening is for the Black Hole to actually be consuming mass to provide this propulsive force.

Having made this assumption I would like to see if this might possibly explain our presently expanding universe.

**Another calculation we can do is to determine how far a mass would travel if it was subjected to the repulsive forces presumed to be emanating from the axial ends of the mass rotating at the center of our galaxy.**

Let us assume that a mass equal to that of our solar system is sitting at a distance just beyond where the rotational forces of the rotating center are greater than the Newtonian gravitational forces.

We know that F = ma where **F** is the force, **m** is the mass the force is acting on and **a** is the acceleration being experienced by this mass.

a = F/m

a = dv_{s}/dt

If we integrate we get

v_{s} =( F/m)*t + v_{o}

Where v_{s} = velocity of above mass

v_{o} = initial velocity

Knowing that v_{s} = dx/dt and F = G/(c^{2} *2*D)*.2*M*V^{2} *m/x

x = distance travelled

Then

x dx/dt = G/(c^{2} *D)*.4M*V^{2} *t + v_{o}

Let us assume that v_{o} = 0

Integrating and transposing we get:

x^{2}/2 = G/(c^{2} *D )*.4*M*V^{2} *t^{2} /2 + x_{o}

x = (G/(c^{2} *D )*.4*M*V^{2} *t^{2} + 2*x_{o} ) ^{0.5}

t = time traveled

Assuming v_{o} = 0 is most certainly a bad assumption as it would be expected that at a time not to long after the big bang that v_{o} would in all likelihood be close to that of the speed of light. However, in light of not knowing what it was we’ll assume it to be zero.

x_{o} is essentially 0.

During the early age of the universe and the scale of distances we are looking at today, this is probably not a bad assumption.

If the age of the universe is 14 billion years and we insert this than we would calculate the distance traveled from the start of the universe to be **27 million light** years. This is obviously not sufficient to get out to the 14 billion light years we presently see. However, if we use a mass 500 times that of the black hole at the center of our Milky Way and a rotational velocity of 1.67% of that of light or using the mass to be the same as presently in our milky way and a rotational velocity of 37% the speed of light we start to get numbers much closer to that of the 14 billion light years that is the presently accepted age of the universe. In any case this is speculation at this point in time.

The other issue with this hypothesis has to do with the narrowness of this negative gravitational force. It must be in the form of a cone emanating from the axis of the black hole. This would cover only a small part of the volume of the universe and could not explain how all parts of the universe seem to be expanding uniformly. However if we look at the number of galaxies in the universe and assume a random distribution it is quite easy to determine that there are a sufficient number of galaxies to cover every cubic centimeter and thus this expansive force would be distributed relatively evenly.

It does show that this hypothesis (although maybe not probable) it is a possibility.

**Explaining the Observed velocity data of star systems traversing the Milky Way**

**Graph of Orbiting Star Systems in the Milky Way vs Their Distance from the Center of the Galaxy**

The explanation of the above graph is as follows:

**Why is the velocity curve flat at a certain distance out from the center of the galaxy?**

The velocity of star systems remains flat due to the fact that at a certain distance out from the center of the galaxy the rotational gravity force is greater than the Newtonian gravity force and since it varies with 1/R rather than 1/R^{2} it would be expected that objects further out would maintain a constant rotational velocity.

**Why does the velocity curve drop off so sharply as one approaches the center of the galaxy?**

It is suspected that what happens here is that the density of the stars and thus the mass density becomes sufficient such that the interplay of their mutual gravitation forces them to move in lock step. Thus their angular orbital velocity becomes fixed and their actual velocity varies directly with their distance from the center of the galaxy. Thus if you look at the curve you can see that at four (4) light years the velocity is approximately 245 km/sec. Thus one would expect that at one and one half (1 ½) light years (last measured point on graph) that the velocity would be approximately 92 km/sec. This seems like a very good approximation of what is observed. This would eventually breakdown as the star systems approach the center of the galaxy (perhaps close to the event horizon) and everything would then tend to speed up.

**Dark Energy**

**Where does the energy come from to explain the expanding universe?**

What can we learn from recent data in regard to the accelerating expansion of the universe?

The following is some of the recent information that has been learned.

1. The universe is expanding at a rate of 74.3 km/sec for every mega parsec (approximately 3,000,000 light years). This translates into an acceleration rate of 7.85E-10 m/sec/sec.

2. The acceleration seems to have started approximately 5,000,000,000 years after the big bang.

From this information it is possible to estimate the Mass of the universe at this point in time.

The force necessary to generate this acceleration of a certain mass = F = ma,

Where:

F = force in newtons

m = mass being accelerated and

a = the acceleration of the mass in question.

M = mass of universe

Likewise the force at 5 billion light years opposing this expansionary force would =

F = G*M*m/r^2

Assuming that these two forces are equal at 5 billion light years we get:

F = G*M*m/r^2 = ma

m cancels on both sides of the equation and we can calculate the Mass of the universe at this point in time.

Thus: M = a*r^2/G

Inputting the data at 5 billion light years we get M = 2.62E+52 kg.

This compares to present estimates of 6.17E+51 kg (not including dark matter estimates).

This shows a discrepancy of 1.94E52 kg between now and 5 billion years ago.

What happened to this extra mass?

**Can this missing mass account for the accelerating universe?**

What is causing the universe expansion to be accelerating and where does this extra energy come from.

We can use the previous data to access the order of magnitude of energy that might be required to accelerate the expansion of the universe.

The energy required to accelerate a given mass from the 5 billion light year mark to the 14 billion light year mark which is the accepted age of the universe is as follows:

Where E = energy – joules

F= Force (newtons)

R = distance from 5 billion light years to 14 billion light years or 9 billion light years.

m = a given mass

a = acceleration

E = F*R = m*a*R

Thus E = m*7.85E-10*8.51E+25 (joules)

Where does this massive amount of energy come from?

There seems to be three possibilities:

1. There is energy being transferred into our universe from a source outside our universe. (a part of the multiverse hypothesis)

2. Space itself has some inherent energy built into it that can be transferred to kinetic energy.

3. I’d like to offer another possibility. The energy required for this kinetic energy comes from some form of “engine” that can transfer the energy located in mass itself into the presently observed kinetic energy.

We know from Einstein’s equation that mass contains the following amount of energy:

E = m1*c^2

Where:

E = energy – joules

m1 = a given mass

c = speed of light.

For purposes of this discussion let us determine the fraction of mass that would have to be converted to energy to allow m to accelerate over 9 billion light years.

Thus:

The fraction of mass to be converted would = m1 /m = 7.85E-10*8.51E+25/c^2 = 0.74 or 74% of the mass would have to be converted to kinetic energy.

If we apply this to the total mass of the universe than 74% of the mass of the universe would have to have been converted to kinetic energy in order to maintain the law of conservation of mass and energy.

This means that 74% of the 2.62E+52 kg would have to have been converted over the 9 billion years. This amounts to 1.94+52 kg.

If we subtract this from the 2.62E+52 we get 6.52E+51 kg.

This is remarkably close to the present estimate of the mass of the universe.

It is important to note here that this is not necessarily proof of this hypothesis as the estimates of the mass of the universe are subject to large margins of error. However, it does suggest that this proposal bears some further investigation.

The question now becomes what engine or mechanism might be able to convert mass energy to kinetic energy.

I suggest that one engine for converting mass to kinetic energy might again be the spinning black holes located at the center of essentially all galaxies. I have no good logical reasoning for suggesting that black holes are responsible. However, I think it might be worth looking into the possibility that just as I am suggesting that there is a positive gravitational attraction perpendicular to the axis of rotation of the Black Hole, I also suggest that there may be a negative or repulsive force parallel to the axis of rotation of the black holes.