# Quick clarification on Hawking radiation much appreciated

1. Feb 9, 2014

### acesuv

From what I understand, Hawking radiation results when one virtual particle (of the pair) falls into the black hole while the other escapes...

See I understand why the virtual particles don't come back together - because one is created beyond the horizon while the other is not.

But how does this process make the black hole LOSE mass? it seems like a particle is flying into the black hole increasing its mass. only thing i can think of is that the particle which flies into the black hole is anti-matter and therefore cancels out a particle of matter inside the black hole... and then my question becomes why does a black hole prefer to eat anti-matter as opposed to the normal-matter particle?

also a side question: are virtual particles simply opposite charges? i see how it makes sense mathematically that (+1) + (-1) = 0... but i dont understand why charge is what mathematically defines the particle... i am under the impression that virtual particles are anti-matter and normal-matter, so that they = 0 which makes more sense to me because the term "anti-matter" sort of implies something intrinsic about the substance that makes it "negative". so yeah. charges? no?

thanks,
Jordan

ps: have fun deciphering my layman jargon

2. Feb 9, 2014

### Staff: Mentor

It's worth noting that this picture is heuristic and doesn't really match how Hawking radiation is derived mathematically; see, for example, the comments here:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html

That's not quite correct. The particles are created at the same place, just outside the horizon; but one falls in while the other escapes to infinity. The one that escapes to infinity is the one we see as Hawking radiation.

Because the combined energy of the pair of virtual particles is zero; they aren't real particles, they're just fluctuations in the underlying quantum field due to the uncertainty principle. So one of the pair will have positive energy and one will have negative energy. If the one with negative energy falls through the horizon before the particles re-unite, then the hole loses a little bit of mass because a negative energy particle fell into it; and the particle with positive energy becomes a real particle and escapes to infinity as Hawking radiation. Effectively, this process transfers a little bit of the hole's mass to the Hawking radiation particle that flies away.

No, this isn't correct; the particle which falls through the horizon can be either a particle or an antiparticle (a pair of virtual particles always consists of a particle and its corresponding antiparticle, but either one can fall into the hole). The key thing is that the particle that falls in has negative energy. (Note that if the positive energy particle of the pair falls in, no Hawking radiation can be emitted; what will happen in that case is that the negative energy particle will end up falling in too, and re-uniting with the other one beneath the horizon, resulting in no net change to the hole's mass.)

Antiparticles have opposite charges to particles, yes; but just having opposite charge isn't enough to make one particle the antiparticle of another. All the other particle properties have to be the same: for example, an anti-electron (a positron) has opposite charge to an electron, but it also has exactly the same mass, spin, etc. Whereas a proton, for example, also has opposite charge to an electron, but it has a very different mass, so it isn't the antiparticle to the electron.

It doesn't, not by itself; only the entire set of particle properties (charge, mass, and spin are the key ones, but there are others as well) defines the particle.

A pair of virtual particles always consists of a particle and its corresponding antiparticle, as I said above. (Which one we call "normal matter" and which one we call "antimatter" is really an arbitrary choice; there's nothing intrinsic to the particles themselves that makes one "normal" and the other "anti". The particles we call "normal matter" are just the ones we and all the stuff around us happen to be made of.)