What is the mechanism of Hawking Radiation?

For a long time I thought a pair of virtual particles gets created near event horizon (due to uncertainty principle).
Normally they would quickly destroy each other and they never create flashes of gamma photons because always one of the twin particles has positive and the other has negative mass/energy.
But if sometimes a particle with negative mass/energy falls into event horizon the other could fly away as radiation. 
So the Black Hole would lose mass/energy over time.
I think this does not make sense because, wouldn't it also sometimes possible the particle with positive mass/energy fall into the Black Hole and cancel the mass/energy losses?

Another explanation I saw suggested the particle-anti-particle pairs created by gravitational energy near the event horizon,
(because the gravitational energy there is higher than (any kind of?) pair production energy), with both particles having positive mass/energy, one particle escapes as radiation.
And I think another explanation I saw suggested also similar pair production but later matter-anti-matter annihilation and production of outgoing (gamma) photons.
But if so, isn't Hawking Radiation should happen much much faster? (Because of the perfect efficiency of pair production.)

How about this explanation?
Imagine instead of pair production (twin particles with both positive mass/energy), virtual pair production (twin particles with one positive one negative mass/energy).
The particle with positive mass/energy attracted towards the Black Hole.
The particle with negative mass/energy repulsed away from the Black Hole.
The particles with positive energy sometimes create particle-anti-particle annihilations between themselves and create outgoing (gamma) photons.
But if so why the particles with negative energy could not do the same between themselves, create outgoing (gamma) photons with negative energy? (So that energy losses and gains would cancel out.)