[graham.d]

Yor_on, I am not sure we need tbe concerned about geodesics or not. The paths followed by the particles are all undergoing hyperbolic motion (see definition), that is uniform acceleration. The ones in free fall in a straight line to the centre of a spherical gravitating body are, of course, following a geodesic, but orbital ones are not. I don't think this is a key issue, but I may be wrong.

In case other people are wondering why this is not as obvious as it first seems, please take a look at references to this in Google. An example would be searching for the word combination - hyperbolic motion rohrlich - the last word being the name of one of the main contributors to research in this area.

A paper, by Glass, that suggests that questions have been resolved can be found at:
www.arxiv.org/pdf/0801.1528
The maths is not trivial and assumes equations derived in other referenced papers.

[jartza]

When you are driving in a very large circle, and your motor stalls periodically, then we have a situation where we can use the "force is charge squared times jerk" rule.

Here are the conditions of using the rule:
http://en.wikipedia.org/wiki/Radiation_reaction

Because jerk vector points sometimes forwards, sometimes backwards, you are radiating, but on the average radiation reaction force is not taking away energy from you.

 

Oh yes, when you start braking, radiation reaction force points backwards, and you move forwards, therefore you lose energy and momentum.

When you stop braking radiation reaction force points forwards, and you are not moving much, therefore you you gain the momentum back, but you don't gain the energy back.

[graham.d]

Jartza, I have read the link on this now. I had not heard the word "jerk" used to described the time derivative of acceleration, but I see that it is a sometimes used word for it. I understand the point you make and see that it refers to the Abraham-Lorentz force (or relativistically, the Abraham-Lorentz-Dirac force). This force applies only to periodic motion, which is an assumption required to reach the solution given. If this is the case then to maintain periodic motion this must imply that there needs to be external energy imparted to the charge in order to maintain its motion (if radiating) I think. I would assume, in the case of a cyclotron, this is exactly the case. In a charge orbiting in a radial gravity field this cannot provide an exact solution - if the charge is radiating there will be energy lost and the orbit lowered, so then not satisfying the criterion of periodic motion but only of "damped" periodic motion. However I expect this is close to what actually happens.

So what happens to a directly falling charge (following a geodesic radially in a gravitational field)? This is not covered by this theory but, I assume, will radiate to infinity (Larmor) but not to a comoving observer (equivalence principle). I still have problem with where the energy comes from except by using the slightly mysterious Schott energy theory.

[Soul Surfer]

All Uniformly accelerating and orbiting charges do radiate both electromagnetically and gravitationally.  This can be observed in conditions where moving plasmas interact with magnetic fields like the Crab Nebula (M1)  the electrons orbit smoothly and uniformly around the magnetic fields (Cyclotron orbits) and emit radio waves.  This is also done in the magnetron in a microwave oven  the electrons orbit in a magnetic field and the orbital frequency produces the radiation.  In both of these cases there is very little higher order differentials in the electron velocity.

An electron orbiting the earth under gravitational attraction will radiate electromagnetically and lose energy but at a very low level and low frequency.    All orbiting gravitating bodies radiate gravitational energy as gravity waves but these are of such a low level and low frequency they are undetectable but the theory of the energy loss has been proved with great precision using a pair of orbiting pulsars.

[graham.d]

SS, I am gradually getting a better understanding of this though there are many aspects not wholly clear and much of the maths very daunting, often referring back to other derived equations. What is your opinion of what happens in the case of an orbiting, evenly distibuted line of charge? I know this is hypothetical and not stable, but nonetheless can be thought about. In one sense it should lose energy because it is an array of single charges, each of which will lose energy but, from another perspective it should just create a static magnetic field. And how does this relate to rotating spherically symmetric (charged) systems which do not radiate gravitationally or (I think??) electromagnetically.

[yor_on (OP)]

Graham, you might like this one. The Rindler Horizon.

[jartza]

You know why charge falling into dense and small sized massive object radiates?

Because part of electric field is hanging outside of the gravity field, so to say.

 

[graham.d]

Yor_on, it may take me a while to read that paper. I had not even got on to black holes in this thread. Looks fun though.

I don't understand what you mean, Jartza. Are you talking about a charge falling into a black hole or any gravitating body? How is part of the electric field outside the gravity field?

[jartza]

I guess I mean that tidal forces stretch the electric field.

Black holes, especially small ones, distort the electric field of vacuum, which produces Hawking radiation. Oh yes on the thread about Hawking radiation it was mentioned that tidal forces pull apart virtual particle pairs.

So I would guess there is radiation when electron's electric field gets mangled by gravity.

 
By the way:
What if we place a black hole between capacitor plates, and connect the capacitor to alternating voltage source? 

[graham.d]

I'm not sure about some of these issues. The observed effects will depend from where you are viewing and certainly your relative velocity and acceleration. A BH will suck in charge, as well as anything else, and the BH would end up as a charged BH. Because a non-rotating BH should not "have any hair" the charge's field lines should emanate perfectly radially and evenly distributed. I don't see why there should be any radiation except during the falling in of the charge which, from a distance, will take forever.

The capacitor plates idea is beyond my current understanding (no pun intended). I guess it is not possible to polarise the BH and I would assume then that the dielectric constant of the BH is zero - all the effective field lines from the plates would have to bend around the BH making the capacitance lower than would be the case if the BH wasn't there. I will build one in my garden and measure it :-)

[jartza]

What I really meant was: charged object free falling non-uniformly, while different parts of its electric field being in different gravity fields.

[yor_on (OP)]

I asked him about it, and he sent me this link Graham Black Hole Thermodynamics and Statistical Mechanics by Steve Carlip. I hope it will make it more understandable for us. 
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It looks really nice.

[jartza]

The capacitor plates idea is beyond my current understanding (no pun intended). I guess it is not possible to polarise the BH and I would assume then that the dielectric constant of the BH is zero - all the effective field lines from the plates would have to bend around the BH making the capacitance lower than would be the case if the BH wasn't there. I will build one in my garden and measure it :-)

Oh yes, black hole moving slowly through electric field gently pushes the field lines off of its way. Only a small wave is produced.

Black hole does NOT eat a hole in the electric field that it goes through.

[imatfaal]

I asked him about it, and he sent me this link Graham Black Hole Thermodynamics and Statistical Mechanics by Steve Carlip. I hope it will make it more understandable for us. 
==

It looks really nice.

They look great - Thanks Yor-On