In a very special,"Ask a Physicist," we'll hear the true story of doomed romance of particles and anti-particles as they attempt to defy the undeniable attraction of black holes. It's a story of betrayal, quantum fluctuations, and eventual evaporation.
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Since this is io9, you probably know a thing or two about black holes. I like to imagine an army of you during "Star Trek" yelling at the screen in unison about the ridiculousness of red matter. So it should come as no surprise that I get some fairly sophisticated questions about black holes really work. This week's question comes to us from Jason Honan who asks:
Why does a black hole lose mass when a virtual particle falls into it?
The universe, even the most boring parts of the universe, is constantly awash in activity. Particles and anti-particles are continuously being created and annihilated, and for the most part, we never even notice. But near black holes, things are very different. Before we delve into the quantum-ness of it all, it might be useful to have a little refresher in black hole physics.
Rather than muck about with charged and spinning black holes, I'm only going to focus on the simplest kind — I have to put caveats like that in there lest the 5th degree black belt nerds call me out on it. And in particular, we only care about one part of the black hole, the "event horizon," the ultimate point of no return. You know the incantation: Beyond that point, nothing can escape. Not even light. The more massive the black hole, the larger this event horizon is. This last detail is going to come in handy later.
For a long while after black holes were postulated, it was assumed that if you set up a black hole and left it undisturbed in space, it would remain completely unchanged with time. Just like bears, they won't bother you if you don't bother them. In general, this is a pretty good attitude to have. There's a popular misconception is that black holes are ravenous killing machines, sucking everything into their gaping maws until nothing is left. If you've seen the After School Special about black holes, you'll know that if our sun were to turn into a black hole tomorrow, we'd continue happily in orbit around it as a giant block of ice.
So while you shouldn't get too close to a black hole or poke it with a stick, the idea was that isolated black holes were perfectly static. But black holes, it turns out, have their own agendas. In 1974, Stephen Hawking made a foray into combining quantum mechanics and general relativity, and showed that particle-antiparticle pairs that were created near the event horizon of a black hole could actually cause a black hole to evaporate, and in principle could allow us to see a black hole directly.
In order to understand how Hawking Radiation works we need to first consider things from the perspective of a particle/anti-particle pair. Normally, when you create a pair, the two want nothing more than to re-unite. And they do so very quickly. One of the big predictions of Heisenberg's Uncertainty Principle is that the larger the amount of energy "borrowed" from the vacuum to make the pair, the shorter they can remain apart.
From the perspective of the particles created near the event horizon, nothing seems particularly unusual, at least not from the outset. The two start off a short distance from one another (another consequence of the uncertainty principle), and even though they're in the strong gravitational field of a black hole, they're oblivious to that fact. It's the same way that you can't tell that you're in a gravitational field if I were to, say, cut the cables on an elevator and you and the elevator went in free-fall down to the earth.
But the particles don't get to remain oblivious for long, just as you'd eventually figure out what was going on when the elevator hit the ground. The two particles started off a short distance from one another. One of them was created slightly below the event horizon, and one slightly above. They can't ever reunite. One particle gets swallowed up by the black hole, and the other flies away to sweet, sweet freedom.
A tale of two particles
Usually when you hear the story of Hawking Radiation, people talk about the two particles as an electron and a positron, since they have to be anti-particles of one another. In reality, it's much more common to create a pair of photons — massless particles of light. The photon, you see, is it's own anti-particle. Either way, fate is extremely fickle, and it's completely random which particle will live... and which one will die.
Here's where we need to get into the nitty-gritty of General Relativity. From a relativistic point of view, energy is very different depending on where you are. Fire a photon from a spot near (but outside) the event horizon of a black hole, and it's going to lose a lot of energy. Someone standing far away really doesn't care how much energy the photon started with, just how much it has when it finally gets far away from the black hole. The same argument goes into reverse. If I throw a penny into a black hole and make a wish, by the time it gets close to the event horizon, it will have gained a huge amount of energy. Frankly, I don't really care how much, since the only contribution to the black hole is the amount of mass or energy (E=mc^2 says that they're the same thing) that the penny had when it was far away. After tossing the penny in, the black hole gains a penny's worth of mass.
There are two effects that play off one another. High energy photons necessarily need to be created very near the event horizon because the uncertainty principle demands it. Remember, high energy means small separation, but in order for Hawking Radiation to work, one of the particles needs to be below the event horizon, and the other above.
On the other hand, the closer a photon is to the event horizon, the more energy it loses on its way out. These two effects combine to give a characteristic energy to the photons as when they're actually observed far away. The larger the black hole, the less energy a typical photon ultimately has, and the "cooler" the radiation appears.
How to grow your black hole
Let's put some numbers on this so you can impress people at your next cocktail party. Or con. Whatever. If our sun were to turn into a black hole, it would radiate at a temperature of about 60 nano-Kelvin, and more massive black holes would be even cooler. This is insanely cold, about fifty million times cooler than the background temperature of the universe. Because heat flows from hot to cold, the radiation of the universe actually feeds a typical black hole. Only incredibly puny ones — less massive than the moon — are actually shrinking these days. Stellar mass black holes won't actually start evaporating until the universe gets fifty million times cooler (and thus fifty million times bigger) than it is now. That won't be for a few hundred billion years or so.
In other words, there's no chance we could actually use Hawking Radiation to see black holes today. They're just too cool. We do, however, see hot material falling on to black holes in the form of quasars, but that's not the same thing as seeing the black hole, itself, and at any rate is a topic for another day.
But forget about that minor detail of a trillion years, give or take, and let's get back to the original question. How is it that the loser particle on the wrong side of the event horizon tracks falls into the black hole, and yet the black hole actually loses mass?
Remember that from the perspective of an observer far away, it doesn't matter how much energy a particle started with. All that matters is how much energy the particle could carry away. A particle created above the event horizon loses most of its energy. A particle created exactly on the event horizon would necessarily lose all of its energy, so would contribute nothing to the mass of the black hole. Any particle created below the event horizon actually has a negative energy (at least seen from far away from the black hole, which is the only perspective that matters), meaning that when it falls in, the black hole actually loses mass. The amount of mass lost by the black hole is precisely equal to the energy of the photon that escaped (with a c^2 for good measure). Tada! We're ready to evaporate.
Your gut reaction is probably that this is all messed up. Shouldn't the "real" energies of the particle and antiparticle matter — the energies they had when they are created? Short answer: no. When we talk about black holes, all we ever care about is the mass seen far, far away. It may seem a terribly self-centered perspective, but relativity can be like that sometimes.
Dave Goldberg is the author, with Jeff Blomquist, of "A User's Guide to the Universe: Surviving the Perils of Black Holes, Time Paradoxes, and Quantum Uncertainty." (follow us on twitter, facebook, twitter or our blog.) He is an Associate Professor of Physics at Drexel University. Feel free to send email to email@example.com with any questions about the universe.