If a charged particle is free falling in the gravitational field-

[Garth]

I agree with the part I have not cited, but not with this cited part above. I do not agree that this frame of reference is really preferred, so I do not see a conflict with the equivalence principle.

The gravitational field of the Earth is weak and the argument becomes rather academic.

However, if we move to a quasar or AGN engine then we are dealing with strong fields surrounding a massive black hole.

These bodies radiate strongly, both from their jets and accretion disks, in different regions of the spectrum up to X-ray emission. Some of the powerful emission is thought to be synchrotron radiation. (Jester S et al. 2006 ApJ 648 900).

Here energy is being extracted from 'the process' of charged particles being accelerated from their freely falling frames by powerful electro-magnetic fields.

In this case the forces acting on the particle, which is moving in the BH's rest frame, are doing work. However, consider the rather artificial situation where the electrostatic and magnetic forces exactly balance the gravitational force and keep a charged particle suspended stationary over the BH.

In this hypothetical scenario a powerful force is acting on the particle accelerating it from its geodesic path, yet no work is being done. Will this particle radiate with synchrotron radiation as all the others are doing?

My answer in this case is no, for otherwise where would the power of this radiation be coming from? All forces are balanced and the particle is at rest in the BH's rest frame. However does not GR suggest that it should be powerfully radiating as it is being accelerated from its geodesic path?

IMHO in this case the rest frame of the BH is a 'preferred frame' because only when at rest in that frame are charged particle's not radiating when under the influence of powerful magnetic and electrostatic forces.

This I understand to be in conflict with the principle of relativity and therefore by inference also with the equivalence principle.

If such a particle actually does powerfully radiate then that would be in accordance with the principle of relativity but contrary to the conservation of energy. This would not be inconsistent with the principles of relativity but it would represent a 'free lunch'!

Garth

 

[Demystifier]

This would not be inconsistent with the principles of relativity but it would represent a 'free lunch'!

There is even a simpler way to get a free lunch from general relativity. Assume, for example, that the matter density of the universe exceeds the critical one, so that one day the universe will start to shrink. This means that it will become hotter and hotter as time passes. A kind of free lunch, isn't it? But of course, this increase of the temperature will go at the expense of decreasing gravitational "energy". I suggest you to think if your example can be reinterpreted in a similar way.