All About Black Holes
Welcome to Black Holes 101. Here it is that I try to put into words what
I recall about a number of books and articles about black holes. Any
error you see here I hope will not affect what I'm trying to convey, and are
due to my faulty memory, and I don't recall why it is faulty.
The Gravity Well
Above is a common graphical representation of a black hole. It was made,
by the way, with the Yorick math language which is freely available and incredibly
powerful. The diagram depicts the deepening gravity well that surrounds a black
hole. In this graph, the hole only goes so far, more like the well surrounding
the Earth, for example. But with an actual black hole the depth of the hole is
infinite (as you might assume, I can't graph that).
All mass in the universe has a similar force of gravity around it, so what's
different about the well around a black hole? The infinity I mentioned is the
Earth, for example, has a finite size. An object approaching
Earth does feel the deepening of the well (well, an object free falls and
doesn't feel it actually, but accelerates because of it).
The object will
stop at the surface of the planet, and end up feeling exactly the
force of gravity that we feel. What we feel, actually, is the interruption of
free fall caused by the electromagnetic rejection of us by the material
beneath our feet, but that's a story for another day.
If one could continue penetrating into the Earth, the well would actually
begin to diminish, reaching nothing at the center. Why? Because as one
descends into the planet, more and more mass accumulates around the object,
and less and less exists between the object and the center of the Earth. At
the center, all of the Earth's mass is now pulling equally at the object from
all sides, giving a net acceleration of zero.
Since a black hole has no size, one never reaches the point where some mass
is "behind" it so to speak. The object just keeps getting closer to
the singularity where the well is deeper, with no limit.
One of the nasty effects an object experiences as it falls deeper and
deeper into the gravity well is that across it's own dimension (in the
direction of the black hole) it experiences different strengths of
gravity. The side closest to the black hole experiences a stronger
acceleration than the side further away. It happens around the Earth too,
but the effect is negligible.
The image shown depicts what happens to a circular object as it approaches a
black hole. As the object slides into the gravity well, the side nearest the
well experiences more acceleration than the side further away.
on the pull of different parts of the object, depending upon their distance
from the singularity, grows as the object falls further into the well. The
result will be to distort the circular object as shown, and eventually
So what actually causes the black hole?
(Taking a deep breath) I'll do my best. The black hole is made possible
because of the unstoppable power of gravity. If you could peer into the
interior of a massive body, what you would see is atoms under tremendous
pressure from the mass pressing in on them. The pressure comes from the mutual
attraction due to gravity of all the particles. Pile on more mass and you
increase the pressure on the internal atoms. In star sized objects the
electrons are forced out of their quantum shells and become a kind of electron
fluid. This is called degenerate matter.
In degenerate matter, nuclei don't have the electron-shell buffers around
them any longer. This allows them to collide, resulting in fusion process as
they clump together. This clumping gives off enormous energy in the way of
radiation and neutrinos. When this process begins, a star is born. For stars
near the size of our sun, far more photons are given off than neutrinos. For
very much larger stars, temperatures rise to a point where the neutrino
production increases dramatically.
The electromagnetic radiation given off by the nuclear fusion interacts with
the electrons as it moves to the surface of the star. The photons may
eventually reach empty space, but because of the numerous iterations a photon
encounters on its journey it may take millions of years for a photon created
near the core to escape.
This constant interaction, being absorbed by electrons and being
re-emitted, results in an outward pressure that stabilizes the star. The
neutrinos are inert, and fly through the mass of the star unabated, resulting
in an energy leak. You can see that if the ratio of neutrinos to photons were
to shift to neutrino production, more energy would leak away. This is what
happens in very massive stars, and it leads to their collapse and subsequent
So the electrons are in a squeeze -- what then?
As electrons are forced closer and closer together, they vibrate more
violently. As the hydrogen in the core of a start is consumed, the outward push
weakens, resulting in an increased gravitational squeeze. This additional
pressure raises the compression on the electrons. It also forces larger nuclei
to collide. The star begins burning helium, then as the helium is consumed,
Electrons, like all other objects, are subject to the laws of relativity,
which states that they cannot move faster than the speed of light. When the
speed of light is approached, the electrons cannot vibrate faster and forestall
increasing pressure. Since the compression now continues unabated, the
electrons are pushed into the nuclei. Electrons combining with the protons in
atomic nuclei create neutrons.
This activity in massive stellar interiors is a discovery made by a young
Indian physicist by the name of Chandrasekhar. He realized that the
relativistic constraints placed on the particles in the stellar interior would
lead to a collapse, as electrons were forced into the protons. As more and more
electrons combine with protons, the size of the star shrinks dramatically, and
the shrinking size further increases the pressure.
Not all stars create enough pressure to force this result. But if a star has
about 1.5 times the mass of the sun, that's its eventual fate.
It can get worse if the star has more mass, about 3 times the sun's mass.
As the interior of a neutron star gets squeezed, it's the neutrons that vibrate
as they are compressed. The vibration creates a balancing force against the
gravity, as it did with vibrating electrons. But neutrons also are subject to
relativistic constraints. When enough pressure is placed on the neutrons that
in their vibrations they reach relativistic speeds, they cannot create enough
pressure to sustain the star.
What happens next? You guessed it, a total collapse of all the mass in the
star -- and a black hole forms. When this collapse starts, nothing can stop it.
The star shrinks to a singularity.
The Event Horizon
I'm sure you've heard of it. I think there's even a movie by that
So what is it?
It's all about escape velocity. I'll bet you've heard of that too. When a
space probe is launched to another planet, it has to reach the Earth's escape
velocity or it will simply fall back to Earth. Make it go fast enough, and it
will escape into free space (well, the sun's escape velocity is another
matter). That velocity is pretty high by Buick standards, about 25,000 miles
per hour, or 7 miles per second.
However, by light or photon standards, that's pretty slow. Light, as you may
recall, moves at about 186,000 miles per second. That makes the Earth's escape
velocity of 7 miles per second only about 0.000038 that of the velocity of
light. Photons have little fear of being imprisoned by the Earth.
Escape velocity has to do with the acceleration of gravity at the surface of
a body. Mars, with it's smaller mass, has an escape velocity of about 11,200
miles per hour, less than half that of Earth. The moon's escape velocity is
much lower, only about 5,300 miles per hour. That's why it took such a big
rocket to get to the moon, yet the tiny LEM had enough juice to get away
from the moon (well, to reach lunar orbit anyway).
A black hole, as I covered earlier, has an infinite gravity well. That means
that to get away from the near vicinity of the singularity would take an
infinite velocity. Nothing can do that.
As one gets further from the singularity, the escape velocity becomes less.
At some distance from the singularity (depending upon it's mass), the escape
velocity reduces to that of the speed of light. (Note that blackholes
don't have infinite mass. They have finite mass in an infinitesimal volume,
which leads to the infinite gravity well)
The shell at that distance around the singularity is the event horizon. It
isn't an actual physical object, but a region of space surrounding the
singularity. Further out than the event horizon, photons can escape capture
(if they're headed away). But within the horizon, even photons cannot escape
to free space, because within that boundary the escape velocity is greater than
the speed of light.
So nothing ever gets out?
The image shown is sort of a hypothetical peek inside a black hole. If you
could peek inside, you might see photons buzzing around. These photons would
get red shifted as they move away from the singularity (the energy loss results
in a red shift). The photons would either be curved away from the even horizon
by the gravity well (if not traveling perfectly away from it), or become
infinitely red shifted. Either way, light (or anything else) cannot escape from
within an event horizon.
Stephen Hawking began considering the quantum events happening in space near
an event horizon. In the vacuum of space there is a kind of quantum foam.
Particle or photon pairs are constantly being created (in pairs, because of
conservation laws). Within a Planck time (an immeasurably short time), the
pairs recombine and annihilate again. The pairs are quantumly coupled, and are
always in particle and anti-particle pairs. Photons are their own
anti-particle, so photon pairs are produced.
These pairs are virtual particles, invisible to the observer. They
can have effects on the real particles in the universe, which is how their
presence is known. On any measurable time scale, nothing is going on in the
foam of virtual particles and photons. The conservation laws are kept by the
virtual particle and anti-particle pair aspect and the fact that the energy
borrowed from the universe in their creation is quickly given back in the
So what's the quantum foam got to do with the black hole?
The red and blue squiggles in the diagram represent what is now called
Hawking radiation. Hawking postulated that if a quantum pair of photons popped
into existence too near the event horizon, it is possible that one might be
headed toward the horizon and the other away. The one being headed toward the
event horizon (the blue shifted one) would be prevented from seeking out it's
virtual partner, so annihilation would not occur. The photon escaping from the
event horizon (the red shifted one) would become visible as a real photon.
Real photons have positive energy.
Conservation laws state that the energy of the pair production must remain
zero. Since the escaping photon appears to the outside universe has having
positive energy, the photon getting absorbed by the black hole has negative
energy. The black hole absorbing the negative energy photon has its mass
reduced by the energy amount of the photon.
Let's see -- a photon is seen escaping from the region of an event horizon,
and the black hole is reduced in mass by the amount of the energy of the
photon. That would appear, for all practical purposes, as a
photon escaping from the black hole. Not a photon actually crossing the
boundary, but the energy of a photon escaping, none-the-less. That's the basis
for Hawking radiation.
So black holes aren't invincible after all. Well, nearly so. It turns out
that massive black holes are bound to collect more matter falling in than
Hawking radiation accounts for getting out. So the big ones really do just get
The really small ones actually emit more radiation than the material they
collect (since material has to get very close to be caught). So the little ones
actually appear very hot, and evaporate.
Putting it all together.
Here's the part that fascinates me. Most
physics, like the classical stuff I've been doing for years, can be done
primarily in one discipline. Building a new engine or a new air conditioner?
You need thermodynamics. A new power plant? It's E&M.
But the black hole enigma runs the range of physics. The energy aspects
touch on thermodynamics, which I didn't really get into here. The mass and
gravity, up to a point, can be understood with Newtonian physics. But the
time-warping aspect of the intense gravity and the collapse is
Then at the core, and even at the event horizon, it's quantum physics that
must be used. The physics of the biggest and the smallest must come together
to understand the black hole. Incidentally, the required merged physics hasn't
materialized yet. So hopefully you feel a bit enlightened, and are beginning
to realize why the black hole is such a focus right now.
The gravity well images on this page were made with Yorick.
The others were made with the The Gimp. I
think they reasonably illustrate what I was trying to convey.
I intended this to be a reasonable and understandable introduction to black
holes. There's much more to know, and many bizarre characteristics of the
enigmatic objects that I didn't discuss. A good example is the time travel
possibilities related to black holes, described in Black Holes and Time
Warps, by Kip Thorne. In his book Kip Thorne gets heavily into the strange
time effects of black holes (and worm holes).