First the obligitory apology for a long post: Sorry.
Ok, I’ve been reading this book over the weekend, and I keep pondering something that seems to have been glossed over in all the reading material that I can get my hands on at the moment. Granted, that’s basically limited to A Brief History of Time and The Universe in a Nutshell, along with miscellaneous material on the net, so I could easily be missing something important.
Specifically, blackholes are supposed to emit radiation and simultaneously lose mass. The reasoning being that empty space isn’t really empty - there are tiny fluctuations in the electromagnetic, gravitational, weak force, etc. fields that can be thought of as a pair of “opposite” particles that appear and then annihilate each other so quickly that we can’t directly detect them, and in normal large-scale situations, their net effect is esentially nothing. However, close to the event horizon of the black hole, one of them can fall in and be unable to escape. Thus its partner is set free from the mandate to annihilate with it and can (depending on it’s velocity) escape from the region just outside of the event horizon. This is the radiation that black holes should emit. Fair enough.
As the black hole emits radiation (or rather, as the not-so-empty space near the event horizon emits radiation), the black hole should lose mass. There’s no such thing as a free lunch, after all. The explanation of this phenomenon is where there seems to be a leap of logic that I just don’t follow. Looking at the virtual particle pairs in more detail, they are complete opposites of one another. If one has a left-handed spin, the other is right-handed. One is matter, one is anti-matter. And, perhaps most interesetingly, one has positive energy, and the other has negative energy (anti-matter is not the same as negative energy!). So you might have a left-handed positive energy electron and a right-handed negative energy positron that briefly exist and then bop into one another and annihilate, leaving nothing left over. This is unlike the collision of a particle and and anti-particle which both have positive energy, which will produce gamma rays, if I’m not mistaken. At any rate, Hawking argues that the black hole will lose mass because it is absorbing the negative energy while radiating away the positive energy particles. But the unspoken assumption is that for some reason, only the particles with negative energy will fall into the black hole, or at least that on average, more negative energy than positive energy crosses the event horizon. I’ve been pondering this for a few days, and I just can’t figure out why this should be.
If the fields are truly random (and since their presence is only “required” by the uncertainty principle, this would have to be the case), it would seem that there would be equal probability of the negative particle falling in as the positive particle falling in. In fact, when you look through the illustrations in both of these books, you’ll see that the illustrator went through the trouble of making sure that he never depicted a postive particle falling into the black hole, and yet Hawking has nary a word to be said about this strange phenomenon. It seems that the black hole should absorb an equal number of each, and that it’s mass should stay the same. The radiation would be an equal mix of negative and positive energy/mass. Some of these emissions would manage to collide with one another an annihilate, but some of each kind would be sent flying across the cosmos. From the standpoint of entropy, this doesn’t make any sense, and it doesn’t agree with our observations of objects like quasars, which may contain very large black holes, while Hawking’s model does. So I must be missing something.
But the more I think about it, the worse the situation becomes. The particles with negative energy should deflect spacetime in the opposite direction that normal positive energy does. That is, in the rubber sheet analogy, they would cause a convex deflection rather than a concave one. Two negative energy particles would repulse one another gravitionally, whereas a negative energy particle and a positive energy particle would have no net gravitational effect on one another at all. This seems significant in the case of a black hole’s event horizon. This is defined as the region from which light (having positive energy) cannot escape. However, since negative energy deflects spacetime in the opposite direction of normal matter/energy, it would have to travel just a little bit closer to the center of the black hole before it would achieve a steep enough curvature that it would not be able to escape. It would seem, then, that our poor positive energy virtual particles would be more likely to take the plunge than the negative energy virtual particles. Or, if you want to think about it slightly differently, there would be a very small region of space where we could create a virtual particle pair, and where it would be possible for only the negative energy particle to escape. Under these circumstances, it would seem that a blackhole should gain mass over the long run, and radiate mostly negative energy to the rest of the universe.
Is there someone out there who understands these things in more detail and can explain to me why just the opposite case should be true?