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Black Holes 101

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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 difference.

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.

Tidal Forces

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.

The disparity 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 "spigettify" it.

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 Nova explosion.

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, heavier materials.

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 title.

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 annihilation.

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 bigger.

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 relativistic.

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).