Electron radiate when curving past massive body?

[jnorman]

an accelerating electron will radiate, whether due to changing velocity or due to changing trajectory.

question - if we shoot an electron past a massive body in space, and its trajectory curves along the geodesic created by the spacetime curvature of the massive body, does the electron radiate?

 

[jrlaguna]

Very good question... Short answer: it does radiate. See the matter falling in a black hole, for example.

Long answer: Radiation from an accelerated charge is produced because of the need to "update" the electromagnetic field created by the charge when it changes position. If it is moving with constant speed, the "usual" interaction between the electric and magnetic field take care of that "updating"...

In curved spacetime, Maxwell's laws change. Instead of usual derivatives, you use "covariant" derivatives, which just "jump over" geometry. Let us consider a homogeneous spacetime, where curvature is constant. Then the electromagnetic field of the electron may take care of itself, and do the updating correctly. But if it is not... Let's say that the electron gets into a black hole. Then, the electromagnetic field should "know" of this very far away. How? Some "wave" should travel from the current position of the electron to inform the field far away...