Black holes – supplement

Here are a few notes about black holes that I think are interesting, but didn’t fit in my previous post on the topic.

What would happen if…

I asked as an example question “What would happen if you tried to escort a small black hole into a large black hole?”, but I didn’t answer it. Now I’ll try.

I think that, from your perspective, nothing special happens. It would be like escorting any other object into a black hole. You can predict that your small black hole will continue to fall into the big black hole’s gravity well, ultimately to finish merging with it in some unobservable way.

From the perspective of a distant observer, once the event horizons touch, it is inevitable that the two black holes will merge into one, like two droplets of water merging. The observer will see you appear to meet your demise when you touch one of the horizons involved.

One should not attempt to reconcile these two perspectives.

Not black, not a hole

I’ve seen it suggested that “black hole” is a poor name, because black holes are not holes, and they aren’t black. But I think it’s a good name.

Hole: As I asserted in my previous post, from some perspectives, a black hole is literally a hole in space.

Black: A typical black holes it very, very black. Much blacker than the empty space background of the universe. But I must acknowledge that very small black holes are not black at all. How small? I looked it up, and there is a special temperature at which all objects start to glow visibly: about 798 K, known as the Draper point. The mass of a black hole that would have that temperature is about 1.54×1020 kg. That’s about 1/477th the mass of the Moon, or roughly similar to the mass of Pallas, the third-largest asteroid. As far as we know, that’s much smaller than any natural black holes that currently exist. So, calling them “black” seems reasonable. But on the other hand…

Artificial black holes

Just because a particular kind of black hole could not be created by natural processes, does not necessarily mean it doesn’t exist, and it definitely does not mean that we can’t or shouldn’t study it theoretically. Who knows? There could high-tech intelligent alien beings out there constructing or tending unnatural black holes.

Naked singularities

My assertion that a black hole’s point-like singularity does not truly exist comes with a caveat. If a “naked singularity”, i.e. a black hole without an event horizon, is possible, then I would be forced to admit that something like a point-like singularity can exist.

Based on my limited understanding, such a black hole would have to be rotating as fast as the laws of physics allow, and maybe also have a maximal electric charge.

The impression I get is that naked singularities probably don’t exist in this universe. Or at least, they would be so unstable that they don’t exist for any meaningful length of time.

None of this is applies to the simple nonrotating black holes I considered, but still, naked singularities would do my argument no favors.

Density

As black holes get larger and more massive, they get less dense. (I’m referring to “apparent density”: mass divided by the apparent volume.) The biggest supermassive black holes are not particularly dense in absolute terms. If I calculated correctly, a black hole with a mass of 4 billion Suns would be only about as dense as air. Such a black hole would have a radius of about 77 AU, or about the same as the orbit of the dwarf planet Eris. That’s quite big for a supermassive black hole, but there are a few known that are larger.

The Milky Way’s supermassive black hole is “only” about 4 million solar masses. Its density is about one million kg per cubic meter. Its radius is about 0.08 AU, or about 1/5 the radius of Mercury’s orbit.

Hawking radiation and lifetimes

Every black hole emits particles in the form of Hawking radiation. Except for very small black holes, it takes a very, very, very long time for this process to significantly reduce the black hole’s mass.

It’s an unstable equilibrium. Small black holes that are emitting more than they absorb get even smaller and hotter. Large black holes that are absorbing more than they emit get even larger and colder. (However, the universe is cooling down as well, and will eventually catch up to and pass every black hole in the “who’s the coldest” race. So this situation won’t last forever.)

The temperature of the Cosmic Microwave Background Radiation that pervades the universe is about 2.73 K, so any black hole in a natural setting would have to at least be hotter than that in order for it to be getting smaller. I suspect the critical temperature is actually a little higher than 2.73 K, to account for dark matter, and other things. But if we go with 2.73 K, a black hole of that temperature would have a mass of about 4.50×1022 kg, or about 0.61 times the mass of the Moon. That’s much smaller than any black holes that we know about.

A black hole doesn’t have to be very big for it to last a long time. One with the mass of a small mountain could last 10,000 years, shining very brightly the whole time. The lifetime is very sensitive to mass. Whether its lifetime is 100 years, or 1 million years, it’s still in the “mass of a small mountain” category.

References

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