And wash away the rain?

November 2, 2012 10:54 AM

What is the minimum mass that would be requisite to form a black hole?

I realize that black holes are more a function of density rather than volume. Would this mean that theoretically if I could smash one or two atoms into a tight enough space, I could create a singularity?

posted by shakespeherian to science & nature (9 answers total)

In theory, the Planck mass, or about 22 micrograms. So, no, you wouldn't be able to create a black hole with one or two atoms -- you'd need about 22 micrograms worth of whatever atom you had in mind.
posted by un petit cadeau at 11:00 AM on November 2, 2012 [1 favorite]

If you're talking about stars, the Chandrasekhar Limit is a good estimation of what it would take to make a star actually collapse into a black hole.
posted by Zalzidrax at 11:00 AM on November 2, 2012

Physicists (IANAP) have speculated that individual electrons might be black holes. I wouldn't call it a rigorous theory, perhaps more along the lines of a thought experiment, but it's an interesting notion.
posted by Zonker at 11:06 AM on November 2, 2012 [1 favorite]

Minimum mass of a (micro) black hole, is, in fact, the Planck mass, and can we make one? (maybe)
posted by anaelith at 11:27 AM on November 2, 2012

The above answers are slightly misleading. You can get a couple atoms up to the required mass if you get them going at a sufficient fraction of the speed of light (not just 0.9 times the speed of light... you'd need about 18 nines to do it with hydrogen, a little bit less for more massive elements).
posted by Jpfed at 12:22 PM on November 2, 2012

_{Because energy and mass are equivalent (E=mc²), so you can make up lacking mass with extra energy.}
posted by katrielalex at 1:41 PM on November 2, 2012

Jpfed - I don't think that's true. I think what you are implying is that if you get the atom going fast enough then its relativistic mass will be enough to collapse it into a black hole. That's not true. If something is a black hole in one reference frame then it's a black hole in all reference frames (don't ask me why it doesn't work, because the last time I asked that I was bombarded with "stress-energy tensors" and that's way beyond me, but it doesn't).
posted by It's Never Lurgi at 1:44 PM on November 2, 2012

I don't think that's true. I think what you are implying is that if you get the atom going fast enough then its relativistic mass will be enough to collapse it into a black hole. That's not true. If something is a black hole in one reference frame then it's a black hole in all reference frames (don't ask me why it doesn't work, because the last time I asked that I was bombarded with "stress-energy tensors" and that's way beyond me, but it doesn't).

Agreed. Here's a discussion of this from last year.

I should also point out that the answer "the Planck mass" is really just a best guess more than anything else. In General Relativity, Einstein's theory of gravity, there's no minimum mass for a black hole; you can make it as small or as large as you want. We physicists strongly suspect, however, that gravity as Einstein conceived of it will have to be modified in order to describe gravity on really small scales (in other words, to accommodate quantum mechanics.) Most physicists believe this means that there'll be a fundamental change to the laws of gravity once you get down to the Planck scale, but we don't really know what will happen, because we don't yet know how to modify gravity to accommodate quantum mechanics. (For all we know, quantum mechanics will have to be modified to accommodate gravity instead.) So really, the most accurate statement is, "Microscopic black holes with masses less than the Planck mass will probably have vastly different properties than macroscopic ones, if indeed they exist at all."
posted by Johnny Assay at 2:04 PM on November 2, 2012 [3 favorites]

Just to add to Johnny's comment, you'll often hear that "relativistic objects are more massive," which is where I think the confusion about boosting an object till it becomes a black hole is coming from. Really, an object moving faster has a high energy than it would otherwise, and more energy than you'd expect from Newtonian physics. If you interpret this extra energy as "mass," you get very confused.

However, it turns out that the better thing to use is the "invariant mass" which is, as the name suggests, invariant under velocity changes. This is the mass you'd measure if an object was at rest with respect to you, and this is the mass that needs to be sufficiently high to form a Schwarzschild black hole. Boosting to some new frame of reference won't change this. It will change the observed energy, which makes sense, as the object is now moving VERY fast relative to you. However, total energy isn't the thing that was solved for to get the Schwarzschild mass for a black hole, so comparing the total mass in one frame and total energy in another won't get you the right answer.
posted by physicsmatt at 2:12 PM on November 2, 2012