 The dynamic case for an expanding spinning
black hole universe
modified 20110926

John Erich Ebner
Rosman, North Carolina USA
john.erich.ebner@gmail.com
http://blackholeformulas.com/
26 September 2011

Abstract and purpose. We explore a simple classical model of the universe in dynamic equilibrium. Our purpose is to solve the problems of the flat rotation curves of galaxies, prevalence of dark matter in galaxy dynamics and uniformity of the cosmic microwave background. Wiki calls these "unsolved problems of physics." They are shown to be a consequence of this model of the dynamic universe. The age, radius, mass, expansion rate and density of the universe are unambiguously shown to apply to a black hole and are in the range of mainstream values frequently quoted.

Keywords. Spherical universe, black hole universe, rotating universe, black hole formulas, variable gravitational constant, cosmic microwave background, dark matter, flat rotation curves of galaxies.

This is the first of five chapters.
Chapter 1 - The Dynamic Case
Chapter 2 - Black holes
Chapter 3 - Rotation of the Cosmos
Chapter 4 - Dark matter
Chapter 5 - Uniformity of the CMB

Introduction
Bohr's planetary atom and the ring electron are examples of tiny machines which illuminate matter. The realm of the tiny machines was extended to the helical electromagnetic wave. Here we explore a simple classical model of the universe in dynamic equilibrium. It is a machine too. Joni Mitchell in "The Circle Game" sees life as a carousel. Our Cosmos is also a carousel. We are looking out from the inside the carousel and as far as you can see, receding into the distance, are painted ponies. We see the carousel expand as the painted ponies drift apart. Can we see the carousel rotate? Our telescopes haven't seen far enough, to see past the carousel, to see any background against which it might rotate. We are still a ship sailing, on the ocean of the Cosmos, out of sight of land. We must use mechanics and the consistency of the picture painted by math, as science has always done, to infer the rotation of the Cosmos from the rules of dynamics, observations of the CMB, alignment of the rotational axis of galaxies and the polarization of the quasars.

There is a lot of math detail so that the ideas are more accessible. The math is written to be copied into a spread sheet or calculator. One may reason as to its correctness. There is no one above you. You are the authority who must decide. The Cosmos has the radius, mass and density quoted for the observable universe. The Cosmos is an entity which rotates and expands with respect to something larger and outside itself. It is a subset of the universe. The universe is the totality of all things that exist and the source of the material for our Cosmos. Our Cosmos continues to expand and slow in its rotation according to the rules of dynamics.

-->
Postulates or Assumptions
1. Our observable universe is an entity, a dynamic unit. Once you see the expanding spinning black hole universe as an entity as a dynamic unit, it has a more local personal character. You are a part of something. You no longer see it in isolation. It is a ball in play in a much larger game. The Cosmos is the universe regarded as an orderly, harmonious whole. The universe is the totality of all things. Cosmos deals with structure, it has more the clockwork dynamic quality which seems to fit an object of study better than the existential term universe. Here Cosmos will be the name preferred for our local dynamic unit.
2. It is rotating and blowing up like a balloon but very slowly in relation to its size. Like a spinning ice skater slows her spin, by extending her arms, the spinning universe slows in its rotation while expanding.
Click image to animate! Each circle is a cross section of the Cosmos at a different time. The triangle shows the way it expands and rotates. Light orbits at the perimeter of the Cosmos. As the Cosmos increases in size, light orbits farther out. Most observers would look out in any direction and see the Cosmos expanding faster at greater distances. This is a Hubble expansion. We rotate with respect to that which is very far away and is outside our dynamic unit. The length of the hypotenuse of the triangle r is the radius of the Cosmos. It is the velocity of light times the age of the Cosmos, at that particular time, or r = c*age. The hypotenuse expands and has a tangent velocity of the speed of light, v = c. The base of the triangle expands and rotates at its fixed fraction fr of the speed of light, v = fr*c. This fraction "fr" is the cosine of the triangle. We can see that a location, the circled point in the corner of the triangle, where we might be located, expands radially outward and rotates at a constant velocity, proportional to its fraction of the radius of the Cosmos according to the rules of dynamics.
3. Every location within this Cosmos, has a constant tangent and radial velocity which are proportional to its radius. Since the velocity is constant, the acceleration is zero, and no force and no power is required for it to continue on its journey. Energy is conserved.
4. A location spirals out as the Cosmos expands and rotates. The location stays at the same constant fraction "fr" of the radius of the Cosmos r = fr*c*age and a constant velocity v = fr*c. Here fr at the location is .7 and the velocity is, v = fr*c = .7*c. This is a Hubble expanding Cosmos.
Click image to animate! This is another way of looking at the triangles. Light really doesn't orbit, it spirals out. Everything spirals out. Everything spirals apart as the Cosmos grows and slows in its rotation. Spiral galaxies are no surprise if they are part of the Hubble expansion. The Cosmos rotates at c at a radius of r = c*age. Everything has the same tiny angular velocity = v/r = c/(c*age) = fr*c/(fr*c*age) = 1/age = 2.11E-18_1/s, radians per second. Age is the age of the Cosmos. Hubble's constant is also 1/age.
Pluto orbits at v = 4753_m/s at a radius of r = 5.913E12_m. Pluto's angular velocity is v/r = 4753_m/s / 5.913E12_m = 8.038E-10_1/s, radians per second. The Cosmos rotates 831 million times slower than Pluto. This tiny angular velocity will be very hard to detect. The angular velocity was larger in the past. It is changing with a very small angular acceleration = -1/age2 = -4.46E-36_1/s2 or radians per second squared.
5. Our Cosmos has sufficient mass for light to orbit at its perimeter. Orbiting light or energy makes it a black hole universe.
6. From inside the void, left by the departing perimeter, we see the very nearly uniform microwave background radiation also known as the cosmic microwave background the CMB which is low energy light or heat. The CMB comes from the thin spherical region where light orbits at the perimeter of the Cosmos. It is made uniform and emitted by photon-photon scattering. The fact that the CMB appears uniform implies that we might be near the center of the CMB and the Cosmos, an unlikely occurrence, which we will revisit later. The glow of the CMB is dimming since the perimeter's area 4*pi*r2 = 4*pi*c2*age2 is proportional to the age2 and luminosity to 1/age2. The luminosity is decreasing at the same rate as the Cosmos is slowing down in its rotation and increasing in surface area. Its glow is also greatly reduced by the inverse square nature of radiation in its immense travel thru space. It can be described, by the equation for a sphere expanding at the speed of light, like the spherical wave front of an electromagnetic wave with a radius of r = c*age so that x2+y2+z2 = c2*age2 but this is beyond the scope of our simple dynamics.
Hubble (age, radius and radial velocity of the Cosmos)

Edwin Hubble determined from the linear Doppler red shift of galaxies that they are receding at a rate proportional to distance. It is called Doppler because of the familiar Doppler frequency shift of sound with the velocity of the sound source. Here the frequency shift is in the light toward the red with increasing velocity of recession. Think of a sine wave appearing stretched as it moves away. The peaks of the sine wave seem stretched farther apart as it moves away. There is a longer duration between the peaks as the sine wave moves away. The longer duration is the sum of the natural original duration between the peaks of the sine wave plus the duration between the peaks added by the recession of the sine wave. The sine wave seems to have a lower red shifted frequency. The sine wave is unchanged only our point of view and relative velocity has changed. Does space stretch? How could it? Space is empty. How could we see billions of light years with telescopes unless space is empty? Is it more likely that our point of view has changed or that space has changed by becoming stretched? Some people mistake abstraction for reality.

Edwin Hubble determined from the linear Doppler red shift of galaxies that the velocity of recession at a certain distance, divided by that distance is a constant. Hubble's constant, Ho, is about 65 km/(s*Mpc), kilometers per second per million parsecs. In smaller units, this is 2.11E-18_m/s per meter, 2.11 times 10 to the minus 18 meters per second per meter or 2.11E-18_1/s. Using these smaller more familiar units may lead you to wonder if the expansion is also local. Does the Hubble expansion extend to the galaxy, to the solar system, to atoms? If it exists, was it missed because the size of the expansion is so small? Hubble's constant has units of 1/seconds which is frequency, angular velocity or 1/age. The reciprocal of this is 4.74E17_s or 15 billion years more or less, hereafter for clarity, called the age or the age of the universe.

Four examples are;
130_km/(s*Mpc) = 1/7.5 billion years
65_km/(s*Mpc) = 1/15 billion years
32.5_km/(s*Mpc) = 1/30 billion years
16.25_km/(s*Mpc) = 1/60 billion years
At earlier times, Hubble's constant was bigger and the Cosmos was smaller. Hubble's constant is 1/age = c/(c*age) = c/15 billion light years. This implies that the Cosmos is expanding at the speed of light, at its current perimeter, at a radius = 15 billion light years = c*age = 1.42E26_m, the current radius of the universe. Hubble varies, but the radial velocity of expansion vr is constant with distance divided by age or vr = r/age = c*age/age = c. This is age and radius based on the currently observed expansion rate, not an affirmation of a creation event 15 billion years ago. A better choice of origin, for our local dynamic unit, our Cosmos, is growth by accretion, accumulation, clumping and merger which are inherently random and how planets are formed. Merger can not predict an exact time of creation or an origin from a point as does the sacrosanct Big Bang. Merger is a choice, in favor of the mundane and more likely, over the miraculous. The more we know, the less we seem to be the center of the universe.

Binary star systems and galaxies show rotational Doppler red shift. The approaching star in a binary system is more blue and the receding star is more red. The approaching side of a galaxy is more blue and the receding side of a galaxy is more red. The color change is due to velocity. Vera Rubin found that in many galaxies the velocity seen in the red shift spectrum in the rotation of the galaxy does not follow Kepler's laws by decreasing with radius but stays the same at greater radius. The galaxies are said to have flat rotation curves. Radio telescopes extended these flat rotation curves out to the dust clouds that orbit galaxies. We will extend these flat rotation curves even further when we look at an explanation of dark matter.

Non-Doppler red shift is red shift unrelated to the velocity of recession. The much hotter star in a binary system shows non-Doppler red shift. Since the binary stars are receding at a common velocity, the substantial non-Doppler red shift of the hotter star is not due to velocity. The sun also shows non-Doppler solar red shift. There is an unknown ratio between the Doppler and non-Doppler red shift components of Hubble's constant.

• If 1/2 the Hubble constant is due to non-Doppler red shift then the Doppler Hubble constant should be, 32.5_km/(s*Mpc) not 65_km/(s*Mpc) and the Cosmos is 30 billion years old not 15 billion years old.
• If 3/4 the Hubble constant is due to non-Doppler red shift then the Doppler Hubble constant should be, 16.25_km/(s*Mpc) and the Cosmos is 60 billion not 15 billion years old.

The Cosmos must be much older and larger when non-trivial, non-Doppler red shift is included since the calculated radius is proportional to the age of the Cosmos. If most or all of the red shift is non-Doppler and the CMB is the ambient temperature of the star lighted universe, as in the strong case presented by Marmet and Reber, then the universe is infinitely old, large and massive. I assume for now that some of the Hubble constant is Doppler and that the Cosmos slows in its rotation as it expands. The next section might be clearer after reading Gravity, rosettes, binary systems and inertia.

m*vt2/r = G*m*M/r2, this is centrifugal force equals gravitational force, a common characteristic of orbits. The mass of M is usually larger than m. Both masses still orbit across from each other around a common center of mass but this center of mass is close to the center of M.
m*c2/r = G*m*M/r2, substituted c for vt,
Light will orbit with the tangent velocity vt = c at the radius of the Cosmos. We know that gravity deflects light from numerous cases of gravitational lensing so it is not too big a step to see that a deflection of light with one mass could become an orbit of light with a much greater mass.
m*c2 = G*m*M/r, multiplied by r
This is rest energy equals the gravitational energy and a clue that we are on the right track. m*c2 is energy, as is light. Only light and energy orbit at the perimeter at a radius of c*age at the speed of light. Everything else orbits, within the perimeter, at less than the speed of light. Orbiting light makes this a black hole. One could see out of our Cosmos because light can get in, but light can't escape from our Cosmos so it would be black from the outside. m*c2 = G*m*M/r, energy from above.
c2*r = G*M, multiplied by r/m
c2*c*age = G*M, substituted for r = c*age, the radius of the Cosmos.
c3*age = G*Mc, collected c's, M is now Mc, the mass of the Cosmos.
This means that either G, Mc or both increase with age.
G = c3*age/Mc, or
Mc = c3*age /G = 1.91E53_kg = the mass of the universe. If G varies with age the mass is constant. 4*pi2*r3 = p2*G*M, Kepler's third law may be used with r = c*age, the radius of the Cosmos and G*Mc = c3*age, the consequence of an expanding Cosmos with enough mass for light to orbit. p is the orbital period.
4*pi2*c3*age3 = p2*c3*age, substituted for r3 = c3*age3 and G*M = c3*age
4*pi2*age2 = p2, collected terms
p = 2*pi*age = 94 billion years. This is the rotational period of the vorticity of the Cosmos. The period increases as the Cosmos gets older. The axis of rotation of most galaxies line up with a pattern in the WMAP CMB called the "axis of evil" in this "New Scientist article or this Goodness in the axis of evil article. This is according to a study of 1660 galaxies in the Sloan Digital Sky Survey. Rotation has been suggested in the analysis of WMAP data and in the polarization of quasars which also tend toward this axis. These are evidence for the rotation of the Cosmos. Gravitational energy from above with increasing values for r and G is
G*Mc *m /r = c3*age *m /(c*age) = m*c2
We see that the age cancels and gravitational energy stays constant as the Cosmos expands. Power is the rate of change of energy. If the energy is constant then no power is required for the continual expansion of masses which follow the Hubble expansion. centrifugal force = m *vt2 /r = m *c2 /(c*age) = m*c/age
gravitational force = G*Mc *m /r2 = c3age *m /(c2*age2) = m*c/age

Since E = m*c2 then m = E/c2 or m*c/age = E/(c*age)
The orbital forces equal the orbiting energy divided by the radius of the Cosmos. The gravitational energy = m*c2 is constant as orbital forces decrease with age. This allows orbits to increase and spiral out while orbital periods increase and the tangent velocity stays constant.
Inside a fraction of the radius of the Cosmos
r = fr*radius = fr*c*age = distance from the center of the Cosmos to the orbiting mass m. fr is the fraction of the radius to the perimeter of the Cosmos.
vt = fr*c = tangent velocity

m *vt2 /r = G*M *m /r2, the centrifugal force equals the gravitational force.
M = vt2 *r /G, isolate M the mass within the fraction "fr"
M = fr2*c2 *fr*c*age *Mc/(c3*age) = fr3*Mc, where Mc is the mass of the Cosmos and G = c3*age/Mc.

vt2 *r = G*M, becomes
fr2*c2 *fr*c*age = G *fr3*Mc
fr3*c3*age = fr3*c3*age

If fr = .9 then something orbits with vt and vr = .9*c at a radius of .9*c*age while it encloses a mass of .93*Mc or
.92*c2*.9*c*age = G *.93*Mc
.92*c2*.9*c*age = .93 *c3*age
, which confirms the math.

The gravitational energy = G *M *m /r = c3*age/Mc *fr3*Mc *m /(fr *c*age) = fr2*m*c2
The gravitational energy is constant if fr is constant. No power is required for the ongoing expansion.
The centrifugal force = m *vt2 /r = m *fr2*c2/(fr*c*age) = m *fr*c/age
The gravitational force = G *M *m/r2 = c3*age /Mc *fr3*Mc *m/(fr2*c2*age2) = m*fr*c/age
We see that the mass “m” will spiral out while the Cosmos expands with the orbital forces decreasing as m’s orbital radius increases with the age of the Cosmos. As "fr" increases the gravitational force increases so that there is a gravitational gradient.

Density of the Cosmos
The density within a fraction of the radius of the Cosmos is
mass /volume =
fr3*Mc/(4/3*pi* fr3*c3*age3) =
3*Mc/(4*pi*c3*age3) = 1.6E-26_kg/m3 or 1.6E-29_g/cm3
, the fr3's canceled so this average density is the same throughout the Cosmos. The mass of a proton or hydrogen atom is 1.67E-27_kg so the average density of the universe is about ten protons per cubic meter and is decreasing with the cube of the age of the Cosmos. This is in the range of reported values.
References
http://blackholeformulas.com/files/GSJIntroduction.docx
1. Unsolved problems of physics @ http://www.answers.com/topic/unsolved-problems-in-physics#Cosmology_and_Astronomy
2. Bohr's planetary atom @ http://blackholeformulas.com/files/BohrAtom.html
3. Ring electron @ http://blackholeformulas.com/files/RingElectron.html
4. Helical electromagnetic waves @ http://blackholeformulas.com/files/helicalelectromagneticwaves.html
5. Triangle graphic gif @ http://blackholeformulas.com/files/dctri.10.gif
6. Spiral graphic gif @ http://blackholeformulas.com/files/dcconccirc.10.gif
7. Hubble @ http://en.wikipedia.org/wiki/Hubble%27s_law
8. Age of the universe @ http://hypertextbook.com/facts/1999/RachelHoover.shtml
9. Radius of the universe @ http://hypertextbook.com/facts/2002/CarmenBissessar.shtml
10. Non-Doppler red shift @ http://www.newtonphysics.on.ca/hubble/index.html
11. Binary system and solar non-Doppler red shift @ http://www.newtonphysics.on.ca/chromosphere/index.html
12. Marmet and Reber @ http://www.newtonphysics.on.ca/universe/universe.html
13. Gravity theory @ http://blackholeformulas.com/files/gravity.html
14. Mass of the universe @ http://hypertextbook.com/facts/2006/KristineMcPherson.shtml
15. New Scientist @ http://space.newscientist.com/article/mg19425994.000-axis-of-evil-a-cause-for-cosmic-concern.html
16. Goodness in the axis of evil @ http://arxiv.org/PS_cache/arxiv/pdf/0802/0802.3229v2.pdf
17. Sloan study @ http://arxiv.org/astro-ph/0703325
18. WMAP data @ http://arxiv.org/abs/astro-ph/0605325
19. Quasars @ http://arxiv.org/abs/astro-ph/0507274v1
20. Density of the universe @ http://hypertextbook.com/facts/2000/ChristinaCheng.shtml

Goto - Chapter 2 - Black holes