How does Hawking Radiation work?

[Jaami M.]

I'm very new to the understanding of Hawking Radiation. I don't know much about this theory, but I do know that Hawking radiation works on a Quantum scale. I know that with black holes this theory proposes th idea that over time black hole lose mass because of "Spontaneous appearing positive and negative energy particles
Affect the black hole". Negative takes the mass away whil positive manages to escape the black hole resulting in the category of radiation (energy). But how does this all work? And how can particles appear from nothing? I thought "no matter can be created" nor destroyed.

 

[tzimie]

Matter is routinely created and destroyed in particle accelerators.

 

[BvU]

Hello Jaami, welcome to PF !

I take it that like me you did some googling and it didn't help you. (not even http://www.mpa-garching.mpg.de/lectures/ADSEM/SS03_Schmidt.pdf p 16 ?) .
Because of your "And how can particles appear from nothing?" I expect you want some popular explanation, no scientificspeak.

It so happens that particles can appear from nothing, provided their appearance doesn't last all that long. Pretty short, in fact, given that the governing formula from quantum mechanics (google Heisenberg uncertainty principle) is $\Delta E \Delta t \le \hbar / 2$. For $\Delta E$ you can read the energy of the particle concerned, and we don't consider it a real particle but a 'virtual' particle. A few other conditions apply regarding quantum numbers, which restricts this weird phenomenon to particles and antiparticles: they appear out of nowhere (the vacuum is apparently well populated) and annihilate each other almost immediately.

What follows now is my personal picture. I'm not an expert -- in spite of a well-earned PhD in elementary particle physics. Some of the wiser guys will hopefully put me right if I'm completely off track.

In the dangerous neighborhood of a black hole there exists a possibility that one of the two is on the wrong side of the event horizon and flops into the abyss. Then all of a sudden the other is no longer a virtual particle but very real. That's what this sheet 16 tries to bring across. There is a whole construction of thermodynamics and general relativity set up around this and there you need Hawking genius to come to this radiation result. No longer on a quantum scale either ! Hefty stuff because of the huge masses of the run-of-the-mill black holes.