Chapter 2 - Black hole universe modified 20110925
There are two ways of defining a black hole and two black hole formulas. The original black hole definition goes back centuries where gravitational energy equals kinetic energy. It is based on escape velocity from a star exceeding the speed of light. There is more in the appendix.
We have been using a second black hole definition in looking at the Cosmos. Here gravitational energy equals rest energy. It is based on the idea that a black hole has enough mass for light and
energy to orbit. This may be the first time it has been published. This is a simple and logical classical definition. We will continue using this new definition since it answers so many questions.
Go back to Chapter 1 - Introduction
Goto Chapter 3 - Rotation of the Cosmos
m*vt2/r = G*m*M/r2, The centrifugal force equals the gravitational force. vt is the tangent velocity. M and m are masses with the radius r between them. G is the gravitational constant.
m*c2/r = G*m*M/r2, replaced the tangent velocity vt with c, now light can orbit.
m*c2 = G*m*M/r, multiplied by r
The orbiting energy equals the gravitational energy. If G and r both increase at the same rate then the orbiting and gravitational energy are constant as the black hole expands. Energy is
conserved. The tangent velocity is c. Light orbits at the specific radius r. Can light follow an elliptical orbit which requires changes in velocity? Light might follow a circular orbital
path, a spiral path or a bent path as in gravitational lensing. These paths could form a spherical shell or an empty shell since light has energy and consequently mass. Any mass inside
the shell would contribute to the total mass, increasing the radius of the shell. An empty shell of a black hole does requires some thought.
c2 *r = G*M, multiplied by r/m. This is our definition of a black hole or;
c2 *r /(G*M) = 1
c2 *c*age /(c3*age) = 1, substituted the values we calculated in the section on Hubble for r = c*age and G*M = c3*age.
All the terms cancel, telling us that our Cosmos is a black hole.
M/r = c2/G = 1.35E27_kg/m, the current value of the mass per radius ratio for a black hole which decreases with age. A black hole increases by 1.35E27_kg per meter of radius currently but we will see there are lower limits for density and radius.
If G = c3*age/Mc varies with age then r = vr*age must also vary with age, if the mass and c are constant. vr is the constant radial velocity of expansion at its perimeter.
vr *age = M *G /c2, substituted for r = vr*age.
vr *age = M * c3*age/Mc /c2, substituted c3*age/Mc for G, age cancels
vr = M *c/Mc, collected terms, since the age cancels, the radial velocity of expansion is constant and proportional to mass. Black holes expand.
vr = M *1.568E-45_m/(s*kg), or
vr/c = M/Mc
Black holes expand proportional to their mass. The radius of the Cosmos expands at the speed of light c, or 1_light year per year, because it has enough mass for it to expand at c. This expansion is one year in the age of the Cosmos or one part in 15 billion per year currently. This is quite small.
You may have noticed that G has a value of one in 15 billion. It is increasing in proportion to the age of the Cosmos.
- For a ten solar mass black hole or 1.99E31_kg, vr = 3.12E-14_m/s
- For a billion solar mass black hole or 1.99E39_kg, vr = 3.12E-6_m/s. This expands at 98_m/year.
- For a 9.61E22 solar mass black hole or 1.91E53_kg, the mass of the Cosmos Mc, vr=299792458_m/s = c
1/(15 billion) - 1/(15 billion and one).
G = c3*age /Mc, so in a year, deltaG = c3*(seconds in a year) /Mc = 4.44E-21_m3/(kg*s2)
The gravitational force was stronger in the past. How do we detect such a small ongoing increase in the gravitational constant?
c2*r = G*M, after canceling the m's from above
c2*c*age = G*M, substitute for r = c*age.
c3*age = G*M, collect the c's.
We take c and M to be constants. If r is a variable and increases with age then G is a variable and must increase with age. This can be written G = gk*age, G increases with time.
gk = G/age = G*Ho = 1.41E-28_m3/ (kg*s3), gk appears to be a universal constant in contrast to Ho which is Hubble's variable constant and G which is the variable gravitational constant.
c3*age = G*M, from above.
c3*age = gk*age*M,
G increase with age so we can substitute G = gk*age
c3 = gk*M,
we can cancel the age.
c3/gk = Mc = 1.91E53_kg = The mass of the Cosmos. Is mass is due to gravity since that would explain rest energy equals gravitational energy?
force = G*m*M/r2, gravitational force
force = gk*age*m*M/(c*age)2, substituted for G and r the size of the Cosmos.
force = gk*age*m*M/(c2*age2),
force = gk*m*Mc/(c2*age), the force decreases with age. The gravitational force was much stronger earlier. Light from a distant earlier time has a greater gravitational red shift. How does this affect distance calculations? Star formation, accretion and fusion rates would have been affected by the stronger gravitation in the past. The standard candle, Type 1A supernovas would have been affected. What does this do to the accelerating universe dark energy theory?
force = gk*m*c3/(gk*c2*age), substituted for Mc = c3/gk.
force = m*c/(c*age) = m/age, force decreases with the age of the Cosmos for a energy equivalent of a mass at the radius of the universe.
Mc/r = c2/G = 1.35E27_kg/m,
This mass to radius ratio quantifies an energy in orbit black hole at the present time. If the mass is constant and the radius increases then this ratio must decrease with time.
Mc/(c*age) = c2/(gk*age),
expand r and G.
Mc = c3/gk, multiplied by age and collected c's, the mass of the Cosmos does not vary with age but its radius does.
mass = c2*r/G = c2*c*age/(gk*age) = c3/gk, for the Cosmos.
r = mass*G/c2 = mass*gk*age/c2
density = mass /volume
c2*r/G /(4*pi*r3/3) =
3*c2/(4*pi*G*r2), the density decreases with r2.
3*c2/(4*pi*gk*age*c2*age2), substituted for r = c*age.
3/(4*pi*gk*age3), the density decreases with age3 as you would expect.
3*c2/(4*pi*G*r2), from above, substitute for r = mass*gk*age/c2 and G = gk*age
3*c6/(4*pi*gk3*age3*mass2), the density decreases with mass2 or with age3.
Four examples of black hole density using the mass formula;
twenty solar mass = 3.68E17_kg/m3 for a blackhole
ten solar mass = 1.47E18_kg/m3 for a blackhole
five solar mass = 5.90E18_kg/m3 for a blackhole
1.4 solar mass = 7.52E19E19_kg/m3 for a blackhole
1.4 solar mass = 6.6E25_kg/m3 for a neutron star
These are in the range of the density of a neutron star or nuclear density of 10E21_kg/m3 inside the nucleus of an atom, as calculated by particle physicists. The density increases as the mass of the black hole decreases up to a limit and then the black hole is seen as a neutron star not a black hole. Less than five solar
masses is observable as a neutron star not a black hole. Astronomers say neutron stars cluster around a mass of 1.4 solar masses or 2.8E30_kg, and a calculated radius of 9.6 - 11.0_km which gives a density of between 6.9E25_kg/m3 and 6.0E25_kg/m3. The highest density and smallest mass in energy in orbit black holes is therefore nuclear density. The density
decreases as the square of the radius or mass so a larger radius or mass means a lower density. As the mass goes up the density goes down. We have black holes without infinities.
The lowest density black hole is our Cosmos.
Mc/ (4/3*pi*c3*age3) = 1.6E-26_kg/m3 or 1.6E-29_g/cm3
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.
Visualize two spheres that overlap, their contents merge, thereafter being enclosed by a single larger sphere, of their combined diameters. The light and energy in orbit around each black hole, will
after merging, and after their travel through space, eventually orbit at this new larger radius. The light that previously orbited around each black hole will combine to orbit at the new combined black hole radius.
All these photons orbiting at the same radius have many photon-photon impacts which make the very thin layer of photons uniform. Not all of these photon-photon or gamma-gamma scattering's are elastic, many of these impacts emit light which reaches us as the cosmic microwave background the CMB.
While we would expect to see an approaching object to be seen as blue-shifted on the outside of our Cosmos, an approaching black hole emits no light, as all its perimeter light is in orbit. We would only see an approaching black hole when it merged with our own and suddenly appeared inside the perimeter of our Cosmos.
Little ones merge to make big ones. Two soap bubbles merge to make a larger soap bubble. In eggland, two eggs touch. Their shells merge much like soap bubbles merge. Their contents merge. Where there was two eggs, there is now one larger egg with two merged yokes. Over time,
there is a very big egg with many yokes merged together. The yokels, being unaware of the mechanics of merging, make up odd stories of their creation and their importance to the creator.
There are groupings of mass in space so great, that gravity in the age of the Cosmos, would be inadequate for their formation from hydrogen gas. These are called large-scale structure. An example is the Sloan Great Wall.
Their great mass should have been reflected in the observed inhomogeneities in the CMB, if the conventional theory is right.
The merging of black holes, does however, explain these structures. The smaller black hole has a much higher density. The merged contents are
enclosed in a much larger volume. From within, one sees only the merged contents. The smaller black hole leaves behind a higher residual mass density, in the stretched out, merged contents, which is the
artifact or footprint of their merging.
M/r = mass/radius = c2/G = 1.35E27_kg/m
radius = r = mass *G/c2
surface area = mass2 *4*pi* G2/c4
volume = mass3 *4*pi*G3/(3*c6)
density = mass /volume = 3*c6/(mass2 *4*pi*G3)
Two times mass equals; two times radius, four times surface area, eight times volume, density divided by four, and two times vr.
Spherical caps of merging spheres: See the figure above.
A spherical cap is a part cut off a sphere. When two spheres merge they create a lense shaped merged region. The volume of the lense shaped merged region includes twice the volume of the spherical caps of each sphere. The volume of a spherical cap is,
1/3*pi*r3*(3-fr)*fr2, with fr, being the fraction of r, that is the height of the cap. The volume of a sphere equal to four spherical caps would be
4/3*pi*r3 = 4/3*pi*r3*(3-fr)*fr2, or
1 = (3-fr)*fr2, or fr = .6527036
When the spherical caps of merging black holes of the same size reach .6527 of their radius, the volume and the mass of the merged portions satisfies the mass/radius formula for a black
The new velocity distribution in the merged black hole will cause all the orbits to relocate over time but these are small acceleration forces in a low density Cosmos like our own. Light and
energy will eventually occupy a circular orbit at the new now larger radius of the black hole. The masses within will seek their own new orbits. The acceleration at the edge of the Cosmos is c/age =
6.33E-10_m/s2 and is fractionally smaller within the Cosmos. This is billions of times smaller than the acceleration of gravity at the earths surface of 9.8_m/s2. Far from
being a dramatic event, the merging of low density black holes would be hardly detectable from an acceleration standpoint. A black hole approaching ours would be invisible until the merging. Its contents would then become visible in our Cosmos.
When black holes merge they also incorporate a lot of volume and matter which was outside the two original black holes. The material outside the merging volumes would be relatively
undisturbed in large low density black holes. This seems a very natural way for black holes to grow and many stars and galaxies would survive as would the life they might harbor. This is
another level being added to the ancient idea of panspermia or transfer of life between planets or stars as popularized by
Fred Hoyle and others. The viral or bacterial spores in rock can survive for many thousands of years so a super nova, planetary impacts or planetary explosions could spread rock fragments and spores to other planets or star systems. Life could spread across a solar
system, galaxy or merging Cosmos's.
There was a super nova relatively near our solar system around the time that the Earth formed. It left the Earth with its radioactive materials. It would not be surprising if it also left the Earth seeded with life in the form of rocks with embedded bacteria or spores from the nova stars solar system.
There are two ways of defining a black hole and two black hole formulas. In the traditional black hole gravitational energy equals kinetic energy while in the energy in orbit black hole
gravitational energy equals rest energy. The original black hole definition goes back centuries and is based on escape velocity from a star exceeding the speed of light.
If the escape
velocity only equals the speed of light then light will escape. This is the case with the Schwarzschild black hole. The idea with escape velocity is that the escaping object is slowing
continuously and reaches infinity with zero velocity and zero kinetic and gravitational energy.
.5*m*vr2 = G*m*M/r, The kinetic energy equals the gravitational energy. Here vr is the radial velocity, the escape velocity and c. The idea here is that the light has no energy when it reaches infinity. Anyone
closer than infinity might find light with energy remaining and a very visible black hole.
.5*m*c2 = G*m*M/r, if vr = c
m*c2 = 2*G*m*M/r, the rest energy equals twice the gravitational energy.
This demonstrates another aspect of traditional black holes. The energy of the escaping light is twice the gravitational energy, so when the gravitational energy is zero at infinity,
the light still has half its original energy.
m*c2/r = 2*G*m*M/r2, divided by r.
The centrifugal force equals twice the gravitational force, so light can not be restrained to an orbit.
Using escape velocity has problems with the fixed velocity of light,
.5*m*vr2 = G*m*M/r, kinetic energy equals gravitational energy
r = 2*G*M/vr2, isolated r, this is called the Schwarzschild radius in General Relativity.
If r = infinity in the equation above, then infinity = 2*G*M/vr2 which is ok, vr is a variable that goes to zero at infinity.
If r = infinity and vr = c then infinity = 2*G*M/c2 which is false, c can not go to zero at infinity.
Other characteristics of the traditional black hole are:
M/r = c2/(2*G) = 6.73E26_kg/m
c2*r/(G*M) = 2
density = mass /volume =
3*c2 /(8*pi*G*r2 ), using the radius, here the density decrease as the square of the radius not according to mass/volume = mass*3/(4*pi*r3) or
3*c6/(32*pi*G3*mass2 ), using the mass. This equation allows for no change over time. In an expanding universe the density must decrease over time.
Two times mass equals two times radius, four times surface area, eight times volume and density divided by four.
Energy in orbit black holes
Energy in orbit black holes are not the photo-sphere, within the event horizon of the Schwarzschild black hole, where light may orbit because gravity is stronger due to warped
space-time than gravity would be according to the mass of the black hole alone.
The mass/radius ratio of traditional black holes is half that of energy in orbit black holes. This difference may be detectable with the measurement of orbital periods of x-ray emitting
clouds that orbit some black holes in binary systems of a black hole and star as reported, in this edited excerpt from May 12, 2001, Science News.
"The Rossi satellite detected X rays that flicker 300 times per second, from the region around GRO J1655-40. Astronomers would expect this from a blob of hot gas orbiting 64 km from the 6.3
solar mass black hole. Rossi also recorded an X-ray signal flickering 450 times per second. A radiating blob of gas orbiting a black hole is like a lighthouse beacon sweeping past Earth
hundreds of times per second, suggests Strohmayer. The closer the blob gets to the black hole, the faster it orbits. The most rapid oscillation detected by Rossi can best be explained by blobs
of gas that are orbiting 15 km nearer to the hole than indicated by the slower flickering, he says. The material could maintain itself at this closer distance only if the black hole spins,
Goto - Chapter 3 - Rotation of the Cosmos
- Traditional black holes @ http://blackholeformulas.com/files/GSJBlackHoles.html#Appendix
- Hubble @ http://blackholeformulas.com/files/Introduction.html#Hubble (age, radius, radial velocity)
- Nuclear density @ http://en.wikipedia.org/wiki/Nuclear_density
- Neutron star mass @ http://www.lsw.uni-heidelberg.de/users/mcamenzi/NS_Mass.html
- Neutron star radius @ http://www.astro.washington.edu/users/ben/a510/NSTARS.new.html
- Density of the universe @ http://hypertextbook.com/facts/2000/ChristinaCheng.shtml
- Photon-photon scattering @ http://www.hep.ucl.ac.uk/opal/gammagamma/gg-tutorial.html
- Large scale structure of the Cosmos @ http://en.wikipedia.org/wiki/Large-scale_structure_of_the_Cosmos
- Sloan great wall @http://en.wikipedia.org/wiki/Sloan_Great_Wall
- Inhomogeneities in the CMB @ http://www.newton%20physics.on.ca/BIGBANG/Bigbang.html
- Panspermia @ http://en.wikipedia.org/wiki/Panspermia
- Planetary exposions @ http://metaresearch.org/solar%20system/eph/eph2000.asp
- Rossi satellite @ http://www.sciencenews.org/articles/20010512/toc.asp