When is the radiation from an accelerated charge a matter of controversy?

[pmb_phy]

Not conserving photon number is something I have to look at. Their Gibbs free energy is zero, so the is no hindrance to their production or destruction. I can certainly see excavating them out of a quantum backgound as you accelerate through it. But I am not yet sure how this relates to this classical radiation. I could totally wrong, but my prejudice is for an invariant charaterization of this radiation.

The term "conserved" is inaccurate here. I believe pervect means "invariant"?

Pete

 

[Stingray]

I have not heard of "asymptotic matching" could you please enlighten me?

The idea is that if the external perturbations are not too large on small wavelengths, then you can split up the system into three regimes. Call these the near, intermediate, and far zones. In the near zone (close to the black hole), your metric is just a perturbation of the stationary one. In the far zone, your metric acts like a perturbation of the background. Both of these are relatively well-understood problems.

Next, these two perturbation problems are compared in the intermediate zone where they are each approximately valid. They act sort of like boundary conditions for each other in this region, and end up giving a unique solution for the entire spacetime.

In practice, this method is quite difficult to use. The gravitational radiation reaction for a schwarzchild black hole was originally found this way, but generalizing that to charged holes is difficult. I know of someone who tried to do that (Eric Poisson - he has a few papers on the subject), but he gave up because the math got too messy. Still, the method should work if anyone wanted to spend enough time on it.

 

[Rob Woodside]

Thanks Stingray. That's a cute idea, but I can begin to imagine the calculational difficulty. I'll have a look for Poisson's papers at arXiv.

 

[pmb_phy]

Thanks Stingray. That's a cute idea, but I can begin to imagine the calculational difficulty. I'll have a look for Poisson's papers at arXiv.

Hi Rob - I had to wipe by system drive clean, reformat and reinstall my operating system. I lost your e-mail addess. Can you resend it? One of the authors of those papers is a friend of mine. You can talk to him directly since he spent a great deal of time during his career thinking about this.

Please e-mail me and let me know your desires. I can now scan that AJP article in e-mail it when you give me your e-mail address that you have ready access to.

Pete

 

[pmb_phy]

re "S. Parrott, "Radiation from Uniformly Accelerated Charge and the Equivalence Principle", http://arxiv.org/abs/gr-qc/9303025, (2001)"

I recall reading throught that article last week. Parrott assumes something which contradicts a calculation made by Cliff Will in article he wote regarding supporting a charged partilce in a Schwarzschild field.

Pete

 

[Rob Woodside]

re "S. Parrott, "Radiation from Uniformly Accelerated Charge and the Equivalence Principle", http://arxiv.org/abs/gr-qc/9303025, (2001)"

I recall reading throught that article last week. Parrott assumes something which contradicts a calculation made by Cliff Will in article he wote regarding supporting a charged partilce in a Schwarzschild field.

Pete

Thanks very much Pete. I found this and several others at arXiv by searching "accelerated charge". I'm putting together a collection of references for study in the new year.

Amusingly Parrot Starts off by saying it is well accepted that accelerating charges in Minkowski space radiate and it is well accepted that a charge at rest in a uniform gravitational field (Swcharzchild solution) does not radiate.
Ergo Problem Solved.

However. the charge at rest destroys the spherical symmetry of the Swcharzchild solution. Certainly a spherical shell of charge will give NO radiation in the Riessner Nordstrom electrovac around the charged planet. I would have thought that Rindler coordinates for flat space would do a better job of mimicking a uniform gravitational field and Parrot proceeds to use these in the body of his paper. He blames his disagreement with others on different definitions, especially for energy. He feels it is essentially an experimental problem answered by looking at the fuel consumption of a "fanciful rocket" that could either accelerate the charge in empty space or hold it at a fixed radius from a gravitating sphere. He also thinks the equivalence principle too ill defined to make any conclusions. As Andrew said the issue is very much alive.

I screwed up Claudio Teitelboim's name in previous posts and owe him an apology. The edit button on these posts disappears and I can't make the correction.