black hole radiation

[Norman Albers]

This might belong here, or in astronomy/cosmo, but: I read of the possible radiation from event horizon limits of virtual particles, one of which is going outward and the other of which is going in. This may be seen as radiation from the outside but something is gained by the black hole, so it seems to me this cannot be seen as a mechanism for loss of BH mass/energy. What is claimed here? If we have interrupted what was a virtual process. this is serious business, but accounting should go both ways.

[npts2020]

Maybe the mechanism that causes virtual particles doesn't work in extreme gravitational conditions?

[Klaynos]

In a simplistic way, we can imagine vacuum fluctuations causing a particle and anti-particle pair to be created on the event horizon.

 

It is perfectly feasible to imagine one of these (say teh anti-particle) just inside the event horizon, and the other (the particle) just outside.

 

The particle can therefore escape, whilst the anti-particle will annihilate with a particle within the even horizon removing energy from the black hole.

[ajb]

In a simplistic way, we can imagine vacuum fluctuations causing a particle and anti-particle pair to be created on the event horizon.

 

It is perfectly feasible to imagine one of these (say teh anti-particle) just inside the event horizon, and the other (the particle) just outside.

 

The particle can therefore escape, whilst the anti-particle will annihilate with a particle within the even horizon removing energy from the black hole.

 

I have never liked that explanation. Quantum field theory on a curved space-time is a theory of quantum fields not particles. By this I mean we lose the association of states with particles. It is really this that lies behind Hawking radiation.

[Norman Albers]

After annihilation of mass states there is present the same total energy. ajb, is the space necessarily curved? The Schwarzschild solution is of the vacuum with a source. The curvature tensor is set to zero.

 

Maybe the mechanism that causes virtual particles doesn't work in extreme gravitational conditions?

I think the opposite! You can recreate the GR solution by considering the whole thing to be a thickening of the polarizability of the vacuum. Locally one always measures permittivity of [math]\epsilon_0[/math], but you can apply dielectric theory (as in my paper) which has the same weird behavior, only there it's called "dielectric runaway". Maybe the harder question is being approached by ajb who notes that we need to bend our ideas.

 

It seems now that I have had the wrong idea of the word "curvature" so I must apologize to ajb. Checking my sources, one can speak of the rank-4 Riemann tensor. If all its terms are zero then it is a flat, Lorentz space. The Einstein equations use the rank-2 contraction or the Ricci curvature tensor. So the vacuum space outside of a massive source is correctly described as curved. Sorry.

Edited December 3, 2008 by Norman Albers
multiple post merged

[npts2020]

I can't argue with your reasoning, Norman, I am just one of those old fuddy duddies that doesn't like apparent violations of not being able to create or destroy matter. It may turn out that such violations must exactly cancel each other out but if that can be proven false, it would require a major shift in our way of thinking..... well mine anyway.

[Norman Albers]

What cannot be "destroyed" is mass-energy. When an electron encounters a positron, which happens frequently, they "disappear" yielding two gammas going off in opposite directions, balancing momentum and energy. Our local space gives production of "particle-antiparticle" pairs given sufficient energy sloshing around. Each cosmic "ray" in the upper atmosphere creates a large shower of such as it plays pinball with quite a few atmosphere atoms. What is weird is the virtual field, which most of us agree, in some degree, must characterize the "vacuum". Here lie great questions and further theory.

[swansont]

I can't argue with your reasoning, Norman, I am just one of those old fuddy duddies that doesn't like apparent violations of not being able to create or destroy matter.

 

There's no such restriction. CP violations occur that turn antimatter into matter.

 

The key to Klaynos's explanation is that the vacuum fluctuation has less energy than a real particle/antiparticle pair. The additional energy comes from the black hole.

[Norman Albers]

Whoa, thank you Swansont. The plot is thick and I hope to see further. So are all these possibilities expressed in a Lagrangian expression such as I read about the Standard Model? I didn't know how things are structured at this level. You speak of a lower energy of the virtuals; may I call them vacuum fluctuations?

Edited December 4, 2008 by Norman Albers