/sci/ - Science & Math

Its just getting produced at the event horizon, not coming out of the black hole.

>>3615468

Cause something can escape a black hole.

>>3615480
Yes but nothing can escape the event horizon, so what gives?

>>3615493
Nothing can escape from within the event horizon. Hawking radiation is produced at the very edge of it. Two virtual particles show up with one just inside the event horizon and one just outside. The one inside the event horizon gets sucked in and the one outside becomes a real particle; Hawking radiation.

>>3615468
The quantum vacuum (or rather the empty equilibrium state) is not invariant under accelerations, which you experience when not trying to fall (into the black hole). Therefore an otherwise empty state (cyclic vector) appears excited = particle creation.
Writing down a Hamiltonian (time evolution) on a non-flat manifold and/or computing the propagator is a mess. Not having translation invariance (and therefore no obvious energy concept) is one of the main problems of quantum gravity in the classical QFT approach.

>>3615501
Define show up.

When a particle gets sucked inside, a pair is produced and is transmitted outwards by Hawking radiation.
However, why is it that even when no particles gets sucked in that black hole still loses energy via heat?
How does heat radiate outwards?

>>3615513
Everywhere all the time virtual electron-positron pairs are coming into existence out of nowhere then flying at each other and annihilating. At an event horizon is the special case where they can't annihilate. Because Dirac and Faynman.

>>3615506
What's a cyclic vector? I've heard about them, don't understand. Also what's a separating vector?

>>3615548
if V is your vector space, v is any vector in it and you have an algebra A with elements a over the vector space, then a specific vector v0 is cyclic if for all v you find an a in A such that

v = a(v0)

i.e. if you actually only need v0 and the algebra to create the vector space.

thats a definition from the top of my head, might be missing minor details.

In any way, it's a mathematical tool to create the particle space only from the vacuum state v0 and operators, these:
http://en.wikipedia.org/wiki/Creation_operators

see also W3 here:
http://en.wikipedia.org/wiki/Wightman_axioms

How does it work with an electron and a positron?

The positron has positive mass, it would just add mass to the black hole. It seems like it has to be something with negative mass.

Think of it in an 3D environment. The black hole sucks things in, but it will pull things towards a swirl, not unlike you see in a tub when you drain it.

The very top and bottom of the black hole, shoot out giant lasers, if you will. These are the radiation.

Here's what I don't get though, if a virtual particle is created on the even horizon, why does this particle not get sucked back in immediately?

It's not like there's something else pulling that particle away?

What's the dealio?

>>3615615
The particle which falls into the black hole has negative energy with respect to an observer outside the event horizon.

>>3615548

What's our vector Victor?

>>3615602
Thanks, was wondering. I'm familiar with creation and annihilation operators, but there is a whole load of (pure) maths that I'm missing. All this stuff about C* algebras and stuff is so hard...

>>3615642
Sure most will fall back in, but they'll have an energy that follows (say) a Gibbs distribution, <span class="math">e^{-\beta E}/Z[/spoiler], so there will be a few with enough energy to escape.