How does vacuum polarization conserve energy?

[bolognie1]

So just to clear things up before we start, does vacuum polarization occur randomly, or does it just occur when an electromagnetic field is present?
Also, how would vacuum polarization conserve energy - does it take energy from the field or does it emit negative energy gravity waves or something?
Also, in the process of Hawking radiation, what actually happens? Does it absorb an antiparticle and emit the other, or does it absorb one of the photons emitted after annihilation?
Cheers guys.

 

[mfb]

So just to clear things up before we start, does vacuum polarization occur randomly, or does it just occur when an electromagnetic field is present?

The electromagnetic field is always present, but its field strength can be zero.

Also, how would vacuum polarization conserve energy - does it take energy from the field or does it emit negative energy gravity waves or something?

How do you get energy out of it? If you are thinking of the Casimir effect: the energy has been in the finite separation of the objects all the time.

Also, in the process of Hawking radiation, what actually happens? Does it absorb an antiparticle and emit the other, or does it absorb one of the photons emitted after annihilation?

Quantum mechanics happens. Popular descriptions are not what actually happens, but equations are hard to present to the public. "A particle escapes" is probably the best simplified description. No pairs involved.