Why should Hawking radiation decrease a black hole's size?

[nhmllr]

So from what I understand when the particle anti-particle pairs that are constantly being created and annihilated come into existence near a black hole's horizon, the nearer one can get sucked in while the further one can radiate off as though it were heat. And this radiation of energy decreases that black holes mass over time, because of E = mc²

But what about the other particle that went into the singularity. Shouldn't the mass increase?

Thanks.

 

[Drakkith]

The creation of a virtual pair of particles takes enough energy from the black hole to create them. Since only one of the pair falls back in, half of the stolen energy has now been permanently lost from the black hole.

 

[nhmllr]

The creation of a virtual pair of particles takes enough energy from the black hole to create them. Since only one of the pair falls back in, half of the stolen energy has now been permanently lost from the black hole.

Ohh... that kinda makes sense. Wow, that actually makes a lot of sense. Thanks.