system
Given the following post, respond as if you're commenting on Reddit:
human
How does a Black Hole lose Mass because of Hawking Radiation?

I understand what quantum fluctuations and virtual particles are but how does the Black Hole lose mass when a particle or antiparticle that comes into existence at the event horizon falls into it? Wouldn't this require negative energy?

**Follow up question:**

How does a Black Hole "shrink"? Matter falls into the Black Hole all the time and the mass that it loses because of Hawking Radiation isn't really that much, does it only "shrink" at a really low speed when there is no Matter around it anymore? 

**And finally:**

What happens when it finally disappears? Does the event horizon just get really small until it "poofs" away?

Sorry for all the Question, but I hope someone can educate me! :)
gpt
Hawking's heuristic "virtual particle" comment works due to the way space and time (and thus momentum and energy) switch roles inside a black hole. In a black hole, your future is the singularity: the distance between you and the singularity decreases for the same reason that in normal life, the space-time distance between today and tomorrow is always decreasing.

This exchange in space and time is what allows the virtual pair to not violate energy conservation. The negative energy particle crosses the horizon where having negative energy is normal for a real particle (for experts: w.r.t. the Killing vectors of the observer at infinity). Then the positive energy particle becomes Hawking radiation, and the negative energy particle decreases the mass of the black hole.

Please heed Hawking's warning though; this is not a rigorous proof of anything:
> It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally... The real justification of the thermal emission is the mathematical derivation given in Section (2) for the case of an uncharged non-rotating black hole.

For your second question, the area does decrease with mass in the usual way, but for stellar-sized black holes, this is *extremely* slow, so you're correct that they would mostly be absorbing way more than radiating. However, the rate and energy of emission increases with decreasing mass, so small enough black holes emit way more than they absorb.

The final fate of a black hole is not known exactly, since the derivations of Hawking radiation require it to be "large enough." There might be unknown physics, such as the black hole leaving a small remnant behind. However, most sources seem to prefer complete evaporation. The black hole becomes extremely hot at the end, and it would go out with an incredible burst of gamma rays.