Table Of ContentThe Black Hole Universe
By R. J. Treharne
Published by R.J. Treharne at Smashwords
Copyright 2016 R.J. Treharne
ISBN: 9781310437090
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Some Basic Physics
For those of you who are cosmologically challenged or have physics phobia, this short
book is written at a level that should be comfortable for most people. So before delving into
demonstrating how the universe can be thought of as a large black hole some basic physics may
help the background. Most of us know that atoms are comprised of electrons, protons and
neutrons; three of the 12 known basic components of matter. The electron has a negative
electrical charge, the proton a positive electrical charge, and the neutron, as it name suggests, is
neutral or has no electrical charge; which is one of the reasons why the neutron was the last of
the three to be discovered. Like charges repeal each other; for example, protons repeal other
protons. Unlike charges attract. Neutrons, however, have neither mutual repulsion nor attraction.
The specific number of the protons (and matching number of electrons) within in atom determine
the element and its associated chemical properties. Hydrogen has one proton, Helium two
protons, Lithium 3 protons and so forth up to Uranium which as 92 protons.
An atom is comprised of a small core or nucleus at its center usually comprised of both
protons and neutrons (the exception being the lonely hydrogen atom which only has a single
proton). The neutrons usually are equal to or close in number to the number of protons within the
nucleus, and are what help overcome the proton’s repulsive forces, holding the protons together.
Around this proton and neutron nucleus is a cloud of electrons (the number of electrons being
equal to the number of protons). The term “cloud” is used because the electrons are not like
small planets orbiting around a sun, but are more or less like statistical possibilities of an electron
existing everywhere and nowhere at the same time. Yes, a very unsettling idea – welcome to
world of quantum mechanics.
A neutron is essentially a proton (positive charge) combined with an electron (negative
charge). The proton is about 1,836 times more massive than an electron; a neutron, about 1,837
times as massive. Consequently, the bulk of the mass of an atom is concentrated in the nucleus.
Relative to the size of the nucleus, the cloud of electrons is massive; something like the Oort
cloud of comets orbiting our own Sun. From the vantage point of the Oort cloud, at the far edge
of our solar system, the Sun is but a dim point of light not much brighter than most other stars.
There is a lot of empty space between the planets, asteroids and comets orbiting the Sun.
Likewise in an atom there is a small volume of mass, the nucleus, surrounded by a very large
volume of very little mass, the electrons. An atom is mostly nothing but empty space.
When a sun undergoes thermonuclear reaction it basically combine atoms with a few
protons and neutrons into larger atoms containing the combined number of protons and neutrons
into a single atom, a process called fusion. In the process a very small amount of the mass is
converted into energy (E=mc2 stuff). The fusion occurs due to the enormous amount of pressure
and temperature created by the relentless mutual gravitational attraction when a very large
number of atoms (mass) are clumped together. It takes quantity of atoms greater than the mass
of Jupiter, but less than our Sun, to achieve the critical mass threshold to cause the temperature
and pressure needed to induce thermonuclear fusion. The larger the collection of atoms (mass),
the stronger the gravity and thus the greater the temperature and pressure. The more massive the
star the higher the atomic number (number of protons in an atom) it can fuse together to create
new elements. Our Sun, for example, is only massive enough to fuse hydrogen into the next
heavier element, helium. More massive stars can fuse together heavier elements up to iron
(atomic number 26) which is relatively common in the universe (for a heavy element) and very
stable. Beyond that, though, it takes a different process of stellar evolution, a stellar explosion of
very massive stars (a supernova) to produce the heavier natural elements, up to Uranium (atomic
number 92).
The structure of an atom is very strong, retaining its configuration even when two of
them are forced together to fuse into a new heavier element. But if the temperatures and
pressures get high enough, such as a result at the center of a supernova explosion, even the
structure of the atom cannot hold itself together and the electrons are forced into the nucleus and
bind with the protons, The result: nothing but neutrons are left – a neutron “star” is born. A
neutron star could have the same mass of our Sun (which is about 1.4 million kilometers in
diameter), yet only be a few kilometers across. Neutron stars are so dense that a teaspoon
amount would weigh millions of kilograms; really dense stuff. A neutron star could be bright,
but probably not as bright as the Sun, since it is only glowing because of its own heat and not
because of nuclear fusion. If our Sun was replaced with an equivalent mass neutron star, the
planets would still orbit as they do, held in orbit by its gravity.
Neutron stars, as inconceivably dense as they are, are still not the limits of possible
compression of mass in a collapsed star. Even neutrons can only withstand so much pressure
and temperature. Combine enough mass together and even the neutron structure will yield to the
extreme pressure and temperature. When a neutron yields it identity, it collapses into God only
knows – literally. Even physicists only speculate as to what really happens. All they really
know is that all the mass is still there, and consequently so is all the gravity, but it exists in an
even smaller volume of space. So much of the collapse of an neutron star is unknown that what
happens next is simply referred to as a “black hole” – a point in space (and time) that yields
ridiculous conditions where the laws of normal physics as we know them seem to break down.
Gravity is so intense near the black hole’s surface and the gravity is so strong (that is the space is
so warped) that nothing, not even a fleeting light particle the photon, can escape its gravitational
pull. Which is one of the many reasons it is called a black hole, because if you could see it, there
would be no light coming from it; hence it should be black. No one really knows for sure since
no black hole has been seen directly. The point from the surface of a black hole where the light
can no longer escape the pull of gravity is referred to as the “event horizon” which is even larger
than the black hole itself. What is occurring at the event horizon or within the event horizon is
the subject of many debates among cosmological physicists. Perhaps black holes themselves
have different stages of development. For example, once the pressures break down the neutrons
in a neutron star, the next collapse could be into a “quark star” – a stellar body comprised of
nothing but the fundamental particles of neutrons themselves, quarks. And maybe, as the black
hole’s mass continues to increase, even the internal structure of quarks themselves collapse into
perhaps whatever the fundamental structure of quarks are, and then once again to nothing but
pure compressed energy. No one really knows. We don’t even know if the inside of a black
hole is even uniform, homogeneous or even black. What is inside a black hole is a big, big
question.
Black holes with masses equivalent to millions and even billions times our Sun’s mass
are now a well established phenomenon in the universe because of their influence on other
heavenly bodies. Large black holes seem to populate the centers of every galaxy, and may be the
reason why galaxies exist; or, vice a versa. No one knows for sure. There may be other black
holes hovering around, either within or between galaxies. There may even be “mini” black
holes, some as small as the size of an atom wondering around – again, no one is sure. Despite
our ignorance, though, some interesting things have been figured out about black holes, most
notably what size they would be relative to their mass. The relationship is known as the
Schwarzschild radius, as defined through the formula:
2 G M Where: R = Schwarzchild radius
Sch
R = ---------- G = Gravitational Constant
Sch
2
c M= Mass of black hole
c = Speed of light
The Schwarzchild radius is the radius of the black hole. The gravitational constant (G) has been
know since the days of Isaac Newton and basically defines the strength of force of attraction
(actually the ability to curve space) between two objects on known mass and at a known distance
as defined in the formula:
2
F = G (m m ) / r m = mass of first object
1 2 1
m = mass of second object
2
r = distance between objects
G = Gravitational Constant
The value of “G” has a curious value and set of units equal to 6.67428 x 10-11 m3/kg s2, and is
actually a relatively weak force. We often don’t think of gravity as being weak, but relative to
the other known forces (electromagnetism, the strong and the weak nuclear forces) it appears
strong because the other forces are almost always balanced or act at very small distances.
Gravity alone is has no balancing force (no anti-gravity) and is able to act at extreme distances,
so in our universe it seems to dominate.
From the Schwarzchild formula, as one would expect, as the mass of the black hole
increases, the radius also increases, and it does so proportionally. Assuming black holes are like
neutron stars and regular stars we can assume that they are spherical in shape. Then from basic
geometry one could further deduce that as the radius increases the volume increases by a factor
of the cube of the radius because the formula for a sphere is defined as:
4
V = --- p r3
3
Thus, a sphere with a radius of 2 units would have 8 times the volume of a sphere of only one
unit. (23 = 8). What is fascinating about the Schwarzchild formula is that as the mass and radius
both increase, the density actually decreases! For example, let’s say we have a black hole with a
mass 1 billion kilograms. The black hole, if it could exist at that size, would be very, very small.
2 G M 2 x (6.67428 x 10-11 m3/kg s2) (1.0 x 109 kilograms)
R = ---------- = ---------------------------------------------------------------
Sch
2 2
c (299,792,456 m/s)
R = 1.485 x 10-18 meters (smaller than the diameter of a proton)
Sch
Knowing that the volume of a sphere (again, assuming a black hole is a sphere) is V = 4/3 p r3;
the volume of a 1 billion kilogram black hole would be:
V = 4/3 p (1.485 x 10-18 m)3 = 1.37 x 10-53 m3; again, a very, very small size.
Its density (mass divided by volume) would equal:
1.0 x 109 kilograms / 1.37 x 10-53 m3 or roughly
7.29 x 1061 kg/m3; incredibly dense; albeit very small.
Now double the mass of the black hole to 2 billion kilograms and its Schwarzschild
radius doubles to 2.970 x 10-18 meters and its volume becomes 1.098 x 10-52 m3; again very, very
small but four times the size it was before, by volume. Is density becomes;
2.0 x 109 kilograms / 1.098 x 10-52 m3
= 1.82 x 1061 kg/m3; again very dense, but only one-quarter the previous density.
Thus, as the mass of the black hole increases and so does it size, its density decreases.
This may be a hard concept to understand, since it is not like a balloon filling up with air where
the density of the air inside the balloon always stays the same no matter how big it gets. Instead,
in the case of a black hole getting bigger, it keeps getting less and less dense. So then, what
would be the density of a black hole which had the equivalent mass of say the entire universe?
The Universe is a Black Hole
When understanding the universe one has to realize that distance and time are
interrelated; that is, the farther in distance you look into space, the father back into time you are
looking as well. This phenomenon is courtesy of the unique behavior of the speed of light (c)
which, although very fast, does have a finite speed of approximately 299,792,456 meters per
second. It takes light time to travel a certain distance. At close distances, the time difference is
negligible, but at larger distances it does become relevant. For example, our Sun is about
150,000,000 kilometers from the Earth – but it is also about 8.3 minutes away from us in time as
well. Even at the speed of light, it still takes light about 8.3 minutes to traverse the 150,000,000
kilometers. The Sun we see now is actually how it was 8.3 minutes ago; it just took the sunlight
that long to reach us. If the Sun were to instantly disappear, we would not know about it until
8.3 minutes later. In universe size distances, between galaxies, astronomers use the distance that
light can travel in a year – known as a light-year – or approximately 9,460,730,472,580,800,000
meters or 9.46 x 1015 meters in scientific notation. So a distance of one light-year is both a
distance in space and in effect a length of time.
Astronomers have probed the universe and seen galaxies as far away as 13.0 billion years
and most “Big Bang” theories (a subject for later discussion) place the universe’s “birth” at
roughly 13.82 billion years ago; so we are seeing very close to the beginning of time. What
happened in those first few hundred million years of universe evolution is still a subject of
debate, since it cannot been seen. Nevertheless, assuming the “age” of the universe is estimated
at roughly 13.82 billion years, or 4.36 x 1017 seconds; that would translate into a distance of
roughly 1.307 x 1026 meters from Earth to the starting point of the Big Bang.
Now comes the confusing part. One has to put aside their normal notions of spatial
thinking and pure geometry, such as the Cartesian coordinates of X, Y and Z or up, down, left,
right, forwards and backwards. Because, one of stranger qualities of mass and its corresponding
gravity, is that mass distorts or “curves” space. In fact, this curvature of space is what we
interpret as gravity. The Sun warps or curves the space around it and the Earth. The Earth
thinks it is moving in a straight line, but it is actually following a space that is curved by the
mass of the Sun. It is like placing a bowling ball on your mattress then rolling a marble past it.
Because of the deformed shape in the mattress, the marble rolls along a curved surface and is
deflected from what would be normally a straight path. But to the marble, just like the Earth, it
is following a straight line, but through curved space. Thus the Newton laws of motion are
preserved.
Consequently, when we look across great depths of space, we have to realize that the path
the light has traveled to us from some distant galaxy has been curved and bent possibly multiple
times before reaching us. It is like a light beam passing through a fiber optic cable. The fiber
optic cable may have been perfectly straight or it could have been winding through a maze of
pipes going all different directions or even coiled around into a loop somewhere in its length. To
an observer measuring the length of time it look a light beam pulse to go from one end to the
other, all the observer could possibly determine is the length of the fiber optic cable; but not the
true actual distance between the two ends of the cable. Similarly, light from galaxies seen as far
away as 13 billion light-years, may in reality be considerably less distant than they appear or to
use the term “as a crow would fly” distance away. Thus, the only way to know the true distance
between us and some distant galaxy is to be able to observe that galaxy with no intervening mass
(gravitational fields) between us and the galaxy which could alter its path. But for the purposes
of this book, we shall assume that the difference is negligible.
Thus let’s assume then that the limit of the observable universe is roughly 13.82 billion
light-years and hence agree that the distance to the “edge” of the universe is roughly 1.307 x 1026
meters. Now the question is: is this the diameter of the universe or is this the radius? Again, one
has to throw out normal three-dimensional Cartesian coordinate thinking. On the one hand, no
matter which direction we look from Earth, we see approximately 13.82 billion light-years –
which would give you the impression that we are at the center of this humongous sphere, which
has a radius of 13.82 billion light-years, therefore its total diameter would be twice that value.
But, on the other hand, what we see at the end of that 13.82 billion light-year search is the same
thing, in essence the same point in space. How can that be?
Perhaps a way to visualize this phenomenon is to imagine an observer in the middle of
the South Pacific Ocean, exactly on the opposite side of the Earth from the famous landmark, the
Eiffel Tower in Paris France. Now imagine the Eiffel Tower emitting a bright rotating light and
that the light from Eiffel Tower was able to and in fact always followed the curvature of the
Earth as it radiated away from the Eiffel Tower. Now the observer on a boat in the South Pacific
has a very powerful telescope able to see that light. Looking through your telescope the observer
could measure that distance to the Eiffel Tower and that distance would be, as one would expect,
half way around the world, or about 20,000 kilometers. In fact, no matter what direction the
observer looked from the observation point in the South Pacific, they would be able to see the
rotating Eiffel Tower light and thus would always measure the same distance of 20,000
kilometers.
Now if observer did not know about the Eiffel Tower’s special light feature (that it was
confined to follow the curvature of the Earth) and they did not know they were on a curved
surface of the Earth (pre-Christopher Columbus thinking – the world is flat) and simply used that
distance to compute what they thought was the total surface of the “flat” Earth, they would get an
inflated size of the surface area of the Earth. By using the formula A = p r2 for the area of a circle
they would derive a value of approximately 2.5 billion square kilometers. In actuality the
Earth’s true surface area is roughly 510 million square kilometers. The observer would be off by
a factor of about 4.9. Had the observer, however, been able to see directly through the Earth,
they would have realized that the “real” distance to the Eiffel Tower was only 2/p of about 63%
of the 20,000 kilometer distance, or roughly 12,732 kilometers. But the observer, cannot see
through the Earth, only around it. Likewise, we have similar limitations when looking into deep
space.
In fact, no matter which direction we look, we see the same thing, but from a different
point of view. The light from that depth (referred to as “background radiation”) has curved
through space so much that from our point of view it appears to be everywhere. We think of
ourselves as being at the “center” of the universe somewhat like our pre-Christopher Columbus
observer thought he was in the center of his flat “universe.” But our pre-Christopher Columbus
observer was actually displaced from the true center of his universe, the center of the Earth, a
three-dimensional distance in his two-dimensional world that he could not comprehend.
Likewise, we are displaced from our true center of the universe, the center of time, a fourth-
dimensional distance in our three-dimensional world. We think the universe is 13.82 billion
light-years in size and thus 13.82 billion years old; but in reality we may only be a 2/p or some
other fraction of that distance away from the “true” center of time in the universe; no way to
know for certain, since we cannot “look through” the fourth dimension. Regardless of the true
size, from a computational point of view we shall use the age of universe as a valid
measurement, similar to our observer using the distance to the Eiffel Tower as a valid
measurement, but when we compute the volume, just like our observer computing the area, we
need to realize that the Cartesian spherical formula we are using may not necessarily apply
because of the inherent curvature of space.
But for now, we shall assume that the universe follows close to the laws of a Cartesian
sphere and the radius is equal to the observable radius, an estimated 1.307 x 1026 meters. If so,
this yields a staggering volume for the known universe at around 9.343 x 1078 cubic meters; a
very large, but still finite size. Now, if the average density of the universe is known, its total
mass can be estimated. It is believe that the average density of the universe is on the order of
9.47 x 10-27 kg/m3 (only a few hydrogen atoms per cubic meter); mostly nothing – almost a
perfect vacuum. If this true, the best guess of the total mass in the universe would be on the order
of 8.85 x 1052 kilograms.
Now, if all that mass in the universe was compressed into a black hole, how large would
it be?
Using Schwarzschild’s formula:
2 G M 2 x (6.67428 x 10-11 m3/kg s2) (8.85 x 1052 kg)
R = ------------ = -------------------------------------------------------------
Sch
2 2
c (299,792,456 m/s)
R = 1.314 x 1026 meters or roughly 13.8 billion light years!
Sch
So a black hole having the mass of the universe would have a radius equal to the current
best estimate of the radius of the universe and it would have an average density equal to the best
density guess of the universe. Ergo, if it walks like a duck and quacks like a duck, maybe it is a
duck.
Granted, there are a number of assumptions in demonstrating that the universe may be
nothing more a giant black hole; but you have to admit the similarities are uncanny. So, the next
