# Why doesn't a charge in gravitational field radiate (or free fall)?

I have read these questions:

Why do accelerating electrons emit radiation?

Why does an accelerated charged particle emit electromagnetic waves?

How and why do accelerating charges radiate electromagnetic radiation?

https://thecuriousastronomer.wordpress.com/2014/05/13/why-do-accelerated-electrons-radiate-electromagnetic-radiation/

Where the comments say:

If the equivalence principle holds, why doesn’t a charge in a gravitational field radiate?

Does a charged particle accelerating in a gravitational field radiate?

Do electrons emit radiation due to gravity

Can the question of a gravitationally accelerated charge radiation be tested experimentally?

Will a stationary charge in a uniform gravitational field radiate?

None of these talk about whether a charge in a gravitational field will not radiate. Or if they will in free-fall.

These questions say facts about the charge in a gravitational field, and in free-fall but they do not both say whether the charge will emit radiation in either case or both and why not in one case and does in the other case.

Question:

1. Why doesn't a charge in gravitational field radiate?

2. Does a charge in free-fall radiate?

• Isn't it answered in: 1 and 2, (2nd is one of your links): "... switch to the rest frame of the charge, you observe a constant electric field. ... switch back to the inertial frame, you see the field changing with time at each point. This ... corresponds to appearing magnetic fields, and hence radiation. In the presence of gravity the case is absolutely similar. ... switching between non-inertial frames makes a static electric field vary and hence represent a radiation flow."? – Rob Jul 8 '18 at 18:54
• Resolution of the paradox by Rohrlich: "... a falling charge will appear to radiate to a supported observer ... To find the fields of the charge in the supporting frame, the fields of the uniformly accelerated charge are transformed according to the coordinate transformation previously given. When that is done, one finds no radiation in the supporting frame from a supported charge, because the magnetic field is zero in this frame."? – Rob Jul 8 '18 at 19:02
• When I was an undergraduate (1971) our EM lecturer was Rudolf Peierls and he spent two whole lectures explaining why a stationary electron in a gravitational field did not (despite the equivalence principle) radiate. To my shame, I cannot remember much more than that... but this is clearly a significant question. – RogerJBarlow Jul 8 '18 at 21:21
• @ Rob, so you are saying that the free-falling charge will radiate to a supported observer (on the surface of Earth)? But the free-falling charge will not radiate to a co-moving observer? And the supported charge (on the surface of Earth)? Will that not radiate? I know that a charge on the surface of Earth is still moving in spacetime. It is moving in the time dimension. And gravity is the same as acceleration. So the supported charge (on the surface of Earth) will radiate to a free-falling observer, but not to a supported (on the surface of Earth) observer? – Árpád Szendrei Jul 8 '18 at 23:21
• @Rob: Answer by Alexey Bobrick that you quoted is definitely the wrong one, despite being accepted. While the effect described does exist, it is in no way the full explanation. – A.V.S. Jul 9 '18 at 13:25