Dear Straight Dope:
After seeing a Discovery Channel show on astronomy which included an explanation of "Hawking radiation" from black holes, I have a question. If the black hole is radiating away particles, however randomly, will the mass of the black hole eventually cross back over the threshold of infinite density and become "normal" matter again? Will a black hole eventually become a brown dwarf that is visible? Or, do black holes, having at one point crossed the critical threshold, retain their infinite density? So to get down to brass tacks, are black holes forever?
There are two important things to know about black holes. First, they’re weird. But second, they’re not as weird as most people think.
For instance, the gravitational field of a black hole is just like the gravitational field of any other mass. If the sun were instantly replaced by a solar-mass black hole (that is, a black hole having the same mass as the sun), the planets would continue to orbit in exactly the same manner: They would not get “sucked in," despite what many people think. I know you didn’t ask about that, Keith, but it’s a common enough misconception that I thought I would mention it anyway.
And black holes also don’t have infinite density. When we talk about a black hole, we generally mean the entire region inside the event horizon, the surface of no return–to put it another way, the region from which no light escapes. This horizon has a radius called the Schwarzschild radius, which is directly proportional to the mass of the black hole (specifically, Rs = 2GM/c^2, where G is the gravitational constant, M is the mass of the object, and c is the speed of light). You can calculate the Schwarzschild radius for any mass, whether it’s a black hole or not. For instance, the sun has a Schwarzschild radius of about 3 kilometers.
If a black hole has a nonzero volume, then it also has a finite density. Since the radius of a hole is proportional to its mass, its density is inversely proportional to the mass squared. Bigger holes, in other words, have lower densities. For a hole of a few solar masses, this density is greater than that of the nucleus of an atom, but a supermassive black hole such as one finds in the core of a galaxy can have a density more like water, or even air.
So why do people talk about black holes as having infinite density? They’re really just referring to the center of the hole. According to the simplest models, all of the mass is concentrated in a single point at the center called a singularity. We don’t know this for certain, though, since all we can observe about a black hole is what goes on outside the event horizon. For all we know, the internal mass distribution could be anything, so long as it’s spherically symmetrical. In fact, it’s widely suspected that once we have a working theory of quantum gravity, it will turn out that the mass of the hole is concentrated in some small, but finite, region in the center.
Getting back to your question, you spoke of Hawking radiation, a process first described by Stephen Hawking in 1974. According to Hawking, black holes actually have a temperature, and can therefore emit radiation (and lose mass and energy in the process). Eventually, due to this effect, a black hole would evaporate away. A full explanation of the process would be too long for this column, but Hawking gives an excellent description in his bestseller A Brief History of Time. The interested reader is encouraged to head to the local library to read more.
So, what happens when a black hole evaporates? It gets smaller, but it always stays a black hole. In the present universe, it’s impossible to form a black hole smaller than a mid-sized star, but there’s no rule against smaller holes existing. As the hole gets smaller, its density increases, as does its power output: Oddly, the more energy a black hole radiates away, the hotter it
gets, so that near the end, you get an extremely energetic and explosive burst of radiation.
Except that all of this is only good up to a limit. Nobody’s quite sure yet what happens right at the end. The simplest thing to assume is that it radiates away to nothing, but there are a lot of problems with that. For one thing, it gets to the point that it would be emitting particles more massive than it is, which is just as absurd as it sounds, even to physicists. Another possibility is that once it gets small enough, about the mass of a bacterium or so, it stops evaporating and just hangs out like that forever. It’s even been proposed that the first time any black hole anywhere does evaporate, it might leave behind what’s called a naked singularity, and thereby cause the end of the world as we know it. Again, this is a job for quantum gravity. But don’t worry: At the rate that black holes evaporate, we’ve got a few hundred thousand billion billion billion trillion trillion trillion years to figure it out.
Send questions to Cecil via firstname.lastname@example.org.
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