A Black Hole Primer
By Dr. John C. (“Jack”) Adler, as told to Bill DeSmedt
Last time, you’ll recall, we were saying that maybe the key to the Tunguska riddle lies in the nature of primordial black holes, like the one the Jackson-Ryan hypothesis claims slammed into the earth that morning in June 1908.
So, what is it about really tiny black holes formed at the beginning of the universe that, all evidence to the contrary, might help that claim prove out?
We’ll get there, trust me. For now, though, maybe it’s better if we back up a bit and talk about black holes in general. Begin at the beginning, so to speak.
And, for a black hole, the beginning is gravity.
Now, the thing of it is, as forces of nature go, gravity’s just not that much to write home about. Compared to, say, the strong nuclear force, it’s a gossamer — the next best thing to nothing at all. Even plain old electromagnetism’s got it beat hands down. Ever pick up a three-penny nail with a toy magnet? Then you know how even a teensy bit of electromagnetic force can overcome the gravitational pull of the whole earth.
In fact, gravity is almost inconceivably weaker than electromagnetism: about ten to the forty-second power, or a million billion billion billion billion times weaker. To make that more concrete, try the following example thought up by string theorist Brian Greene: if the power in your left arm represented the force of gravity, then in order for your right arm to equal the force of electromagnetism, your bicep would have to extend out beyond the edge of the known universe!
This enormous difference between the two most common forces of nature is a real head-scratcher — a puzzle physicists call the “hierarchy problem.” Recently it’s been suggested that, the extra dimensions featured in string theory might offer an answer of sorts. Unlike all the other forces, you see, gravity wouldn’t be confined to our four-dimensional space-time continuum, but could bleed out into the “bulk,” as the six or seven invisible extra dimensions of reality are called.
If so, then the reason gravity’s so weak in our universe is it’s got to spread itself so thin.
But, getting back on topic here: What you maybe never realized is, it’s that same enormous disparity between forces that makes it possible for a planet like earth to exist in the first place.
Because, when you get right down to it, gravity does have one thing going for it — it just keeps on adding up.
And that’s pretty unique, for a long-range force. The strong and weak nuclear forces, for instance, they’re just too short-range to amount to much over the long haul. Electromagnetism’s got the reach, all right, but it comes in opposing flavors: positive and negative, north and south. That puts a natural upper limit on how strong an electromagnetic field can get before it attracts enough opposite charges to neutralize itself. That’s easiest to see on a subatomic scale: atoms normally have the same number of negatively-charged electrons and positively-charged protons, so they net out neutral. But it’s the same story for all the things built out of atoms, including the universe as a whole.
Gravity, on the other hand, only works one way. Never cancels out, never lets go. Each small chunk you add to an object’s mass can only increase, never diminish, the power of that mass’s gravitational field. Just by an infinitesimal amount, maybe, but still that field-strength is always growing, always pulling just a little bit harder.
In the end, it’s only the fact that electromagnetism is so much stronger than gravity that allows for kind of a Mexican standoff between the two forces. Take away the mutual repulsion of negatively-charged electron shells, and all the normal solid matter we know and love — rocks, trees, dachshunds, us, the earth itself — would implode in an instant into tiny little droplets of degenerate matter, dense as the core of the sun.
But there are times and places where even electromagnetism’s not up to the job: Pack a big enough mass into any one place — we’re talking really big here: say, a planet ten times the mass of Jupiter — and the pressure at the core will exceed anything electromagnetism can stand up to. The electron shells that give macroscopic objects their structural strength just buckle. What started out as nice, solid matter dissolves into this sort of “soup” of dissociated electrons and free nuclei.
That degenerate-matter soup is the first step on the road to making a black hole. But we’re not there yet, not by a long shot. Normal matter’s still got some fight left in it.
Take that super-Jupiter we were talking about. Once gravity overcomes the structural integrity of the planet’s core, it just naturally starts to shrink. It’d keep right on shrinking, too, except compressing matter like that generates heat, and enough compression will heat the planet’s core to upwards of ten million degrees Kelvin. That’s the flashpoint: At that temperature, the free atomic nuclei are moving fast enough to overcome their mutual repulsion and start slamming into each other. The strong nuclear force takes over and thermonuclear fusion kicks in.
Fusing lighter elements into heavier ones releases energy. Massive amounts of energy. Enough energy to push back against the pull of gravity. Enough to light the heavens. Enough to warm the worlds and spark the chemical processes that lead to life, to us.
Enough to make stars.
Things can’t go on like that forever, of course. It takes fuel to keep those fires burning. Hydrogen to start with: A star spends most of its lifetime transmuting hydrogen into helium. Works out well enough: hydrogen’s the most abundant element in the universe, after all. The average star holds enough to chug along for billions of years. But sooner or later it’s got to run out. And, when it does, the squeeze starts all over again.
Once gravitational contraction kicks in again, it raises the core temperature back up to where the fire rekindles. Only now the helium “ash” itself becomes the fuel, fusing into heavier and heavier elements — carbon, lithium, oxygen, neon, silicon. All the while, though (if you can call millions of years a “while”), the star is sliding down the slope of the binding-energy curve, earning less and less from each new element-building transaction, until it bottoms out at iron.
As far as nucleosynthesis is concerned, that’s all she wrote. End of the line: Finis. You can’t wring any more watt-hours out of the process by turning iron into something else. Turning iron into any heavier element actually consumes more energy than it produces.
Which sets the stage for the final act.
At the very end there, gravity can grip hard enough that the core of the star just … collapses — collapses so fast in fact, that it rebounds. You get a gigantic explosion, a nova or supernova. The star puts out more energy in that blink of an eye than it did in a whole lifetime of steady shining. The shockwave is powerful enough to transmute elements wholesale and scatter them all across space. At its dying moment, the star seeds the universe with the building blocks of new worlds and new life.
In the aftermath, the only thing that matters is matter itself: namely, how much matter the explosion leaves behind. If what’s left over is only the mass of the sun or so, no problem: Atomic nuclei have got enough structural strength to bear that much weight. You wind up with a brown dwarf star the size of the earth, so dense that a teaspoon of its stuff weighs as much as a locomotive.
But upwards of one solar mass, things start to get interesting.
The leftovers don’t have to weigh too much more than the sun for the pressure in the interior to mash electrons and protons together. That gives you neutrons. And that triggers another collapse, into a neutron star only a few miles across. All that’s really staving off a final collapse at that point is something called the Pauli exclusion principle, which holds that two neutrons — or two matter particles of any kind, for that, uh, matter — cannot have the same position and the same velocity at the same time. That’ll make the neutrons in our neutron star tend to move away from each other, generating an outward expansion that fights back against gravity’s downward drag.
Bizarre enough in its own way, I suppose.
But the point where the relativity theorists really sit up and take notice is when the supernova “cinder” is more than three times the mass of the sun.
Because, there’s a limit to even the exclusion principle. “Chandrasekhar’s limit” it’s called, after the man who worked it out back in the nineteen-thirties. And, at its heart it relies on that old standby speed-of-light limitation, familiar from special relativity. Because, that means there’s only so fast two particles can be moving relative to one another: Once they’re moving at lightspeed, that’s it.
So, given enough gravity, even neutrons will just cave. And neutrons are the last line of defense. Once they go, the whole stellar mass collapses to what we call a singularity — a dimensionless point of infinite density, infinite space-time curvature, infinite you-name-it.
General Relativity is not just a good idea — it’s the law. And what the law says is that, at bottom, gravity is just geometry. The geometry of space-time itself.
It’s easier to picture if we lose a dimension or two. So, imagine if three-dimensional space was a two-dimensional sheet of rubber. That’d make gravity the measure of how much that rubber sheet deforms when you put a mass on it — less for a marble than for a bowling ball. Drop a planet-sized mass onto that rubber sheet and the nearby space curves in to form a gravity well steep enough for moons to roll in orbit around it. Drop in a sun, and the deformation dips deep enough to trap a family of planets in its folds.
But that same geometry is destiny. When a really massive star dies, the sink-hole around its corpse plunges infinitely deep. The well-walls wrap around and pinch shut, sealing off the remains from the rest of space-time.
Remember Alice in Wonderland, where the Cheshire Cat vanishes, leaving only its smile behind? Well, here, the matter disappears, and only the mass is left. In the process, the gravity gradient grows so steep that nothing, not even light, can escape it …
… which is why we call them black holes.
What a wonderful “teaching pair” you and Jack Adler make! This takes a set of difficult concepts in physics and makes them both understandable and tangible. I’ve enjoyed your Jack Adler trilogy, and this writing as well. Do continue!
Back holes can tell us not only the cumulative mass of the things it has “eaten” over time, but also the angular momentum (spin) and magnetic charge if any. Unlike mass, spin and/or charge are usually present but not required if I understand correctly. Are magnetic monopoles confirmed by experimental observation yet?
M – mass
J – angular momentum
Q – electric charge
Schwarzschild has no angular momentum
and no electric charge J = 0 Q = 0
Kerr does have angular momentum
but no electric charge Q = 0
Reissner–Nordström has no angular momentum but
does have an electric charge J = 0
Kerr–Newman has both angular momentum
and an electric charge
(Note: always be cautious when using Wikipedia as a “source”. It is sometimes just someone’s opinion and not carefully vetted facts. That said, this would seem to be consistent with other resources.)
Whoops — the URL for Matt O’Dpwd’s PBS Space Time didn’t “take” — it’s https://www.youtube.com/watch?v=dw1sekg6SUY
Thanks, Dr. Dey — and, no, I’m not aware of any verified observations of magnetic monopoles “in the wild” — although, as Matt O’Dowd reminds us, they SHOULD exist!
There is a recently published study might of interest in the context of your novels and blogs: it describes modelling of crater morphology of primordial black hole impacts (although the authors suggest that a tiny black hole, like the one you describe in [book:Singularity|437399], would actually punch straight through a planetary body, rather than become trapped).
Thanks for the reference, Khira. And, yes — it took some fiddling to slow the PBH down enough to make gravitational capture an option. The key was making Vurdalak a “black monopole.”