Astrophysics/Black Holes: Friend or Foe?
Dear Mr James Gort,
In my sixth form, we are doing an Extended Project Qualification, which should help us to understand more about what we want to do in the future. I have a huge interest in astrophysics, and especially, the life cycle of black holes and what they can do.
I understand the basics of black holes, but I would really like to know how it would benefit/effect us if a black hole (I know it's not possible in the near future) formed within a close proximity of our Earth. What are the good and the bad consequences of a black hole?
Many thanks, Georgia.
Interesting question! Let me first answer by saying that size matters. If a black hole formed from an object with the mass of the sun and then entered the proximity of the solar system, earth would be in trouble. There would then be, effectively, two "suns", which would obviously affect earth's orbit. Ignoring the other planets, we'd have a three-body problem. The black hole and our current sun would form a double star, and the earth would be in some complicated orbit about both. But the important thing to remember is that, from a gravitational standpoint, the size of the black hole (which would be extremely small compared to the sun or even the earth) wouldn't matter - it's just a body with one solar mass! Granted, not much radiation is given off (other than Hawking radiation) so it would not give the same heat as the sun, but it would affect the earth's orbit almost exactly as if it were solar-size (instead of point size). I say "almost" because the finite size of celestial bodies does affect the celestial mechanics. But not by much. For most purposes, orbits can be calculated quite accurately assuming point-sized masses.
So why would the fact that the intruder is a black hole matter at all? It wouldn't (with the caveats which I described above) unless we got very close to it. Now, a black hole the mass of the sun has only the gravitational attraction of one solar mass. We're not "sucked into" the sun (we're in orbit about the sun), and we wouldn't be "sucked into" the black hole either. If somehow the earth was "stopped" in its orbit, it would, of course, accelerate into the sun simply by mutual gravitational attraction, and the same thing would happen if a black hole was in the region. No difference so far.
But what happens if we got very close to an object? Consider the sun first. If we got very close to the sun (say, the earth's orbit was so perturbed that it the earth actually skimmed the sun's photosphere). Well, the earth's atmosphere would probably be "sucked away" (it would be about 5000 degrees C, and the strong gravitation of the sun would suck away much of the atmosphere. Earth itself would whiz past the sun and would be sling-shotted out to the distant solar system. But a small perturbation of the orbit would cause earth to actually "crash into" the sun. Once it enters the solar atmosphere, frictional forces would slow the earth down, and the earth would eventually make up the heavier elements in the sun's core.
Now consider getting close to our black hole intruder. The Schwarzschild radius of a solar-mass black hole is about 3 km. So we'd have to get very close. If the earth whizzed by with just its outer atmosphere "touching" the black hole, say, 100 km away, then the earth would again be sling-shotted out to the distant solar system. Some of its atmosphere would be "sucked away" (but not as much as in the sun's case, because it would no longer be at 5000 degrees C). But the earth would not entirely be "sucked into" the black hole unless it was "stopped" in its orbit and it fell directly in. But the ONLY part of the earth which couldn't escape the black hole would be the part within the Schwarzschild radius - 3 km. Anything outside that radius certainly has a strong gravitational field (as does the sun), but it's NOT inescapable.
So size matters and distance matters. We could have small-mass black holes and they wouldn't affect us at all. If I had a black hole with the mass of my pen sitting on my desk, I wouldn't even know it. In fact, it would be so small that most matter could not even get to one Schwarzschild radius of its centre. It would actually fall through my desk (since it could slip through inter-molecular forces holding the desk together), go through the floor (which couldn't stop it, either), into the ground, and end up at the earth's core. Nobody would be the wiser. It has no more gravity than a normal pen does - it's just a LOT smaller. And not dangerous unless you get VERY VERY close to it (which isn't easy to do for a small black hole).
I once put a problem on an astrophysics exam - can an electron be considered a black hole? It's certainly small. Does it have a Schwarzschild radius? The answer is "no", but we could have very small mass black holes. They're not really special, since they're small mass.
The real problem comes with large mass black holes. Simply because they have large masses (high gravity) AND it's possible to get dangerously close to their Scwarzschild radii.
That's a long-about way to answer your question. A black hole would no more benefit/affect us than any other comparably-sized mass. Unless we got VERY close to its Schwarzschild radius. Then all bets are off.
Prof. James Gort