How does Hawking radiation work?

[caspeerrr]

When reading about this subject on the internet, I found two ways how it works and I don't know which one is correct.

1:
A particle pair is created near the black hole horizon. So there is an antiparticle and a particle. The antiparticle gets sucked into the black hole but because the antiparticle has a negative amount of energy, the total amount of energy inside the black hole will decrease. The particle will be sent away from the black hole as hawking radiation.

2:
A particle pair is created near the black hole horizon. To create this pair, energy of the gravitational pull of the black hole is used. The particle pair is entangled. One of the two will be sucked into the black hole while the other one will be sent away as hawking radiation. In conclusion, the black hole used the energy to create two particles and will only get the energy of one particle back. So, the total amount of energy will decrease and the black hole evaporates.

Which one is correct?
Thanks in advance!

 

[PeterDonis]

I found two ways how it works and I don't know which one is correct.

Neither one is correct. They are both attempts to describe in ordinary language a process that involves some fairly advanced quantum field theory in curved spacetime (and even those advanced models aren't entirely satisfactory, which is why there are still open areas of research on this topic).

A decent quick summary of the limitations of these ordinary language descriptions, along with a somewhat better ordinary language description, is given in this Usenet Physics FAQ article:

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

 

[Nugatory]

And if you want to see the real thing, here is Hawking's paper: http://www.itp.uni-hannover.de/~giulini/papers/BlackHoleSeminar/Hawking_CMP_1975.pdf