general relativity - Does a charged particle accelerating in a gravitational field radiate?

A charged particle undergoing an acceleration radiates photons.

Let's consider a charge in a freely falling frame of reference. In such a frame, the local gravitational field is necessarily zero, and the particle does not accelerate or experience any force. Thus, this charge is free in such a frame. But, a free charge does not emit any photons. There seems to be a paradox. Does a freely falling charge in a gravitational field radiate?

Answer

The paradox is resolved as follows: the number of photons changes when you switch between non-inertial frames. This is actually a remarkable fact and it holds also for quantum particles, which can be created in pairs of particles and antiparticles, and whose number depends on the frame of reference.

Now, a step back. Forget about gravity for a moment, as it is irrelevant here (we are still in GR, though). Imagine a point charge, which is accelerating with respect to a flat empty space. If you switch to the rest frame of the charge, you observe a constant electric field. When you switch back to the inertial frame, you see the field changing with time at each point and carrying away radiation from the charge.

In the presence of gravity the case is absolutely similar. To conclude, switching between non-inertial frames makes a static electric field variable and corresponds to a radiation flow.

Another relevant point: When moving with charge, no energy is emitted, but when standing in the lab frame, there is a flux observed. However, there is no contradiction here as well, as the energy as a quantity is not defined for noninertial frames.