gravitationally accelerated electron

ardenbook

If I drill a hole through the center of a motionless asteroid,
and drop a charged object down it, If the hole goes all the way through,
the particle will oscillate, speeding up as it moves towards the center,
and slowing down as it moves away. If radiating, we'd expect the
oscillations to dampen as some gravitational potential energy gets
irreversibly converted. But according to "equivalence principle",
the charged object is in free-fall and should not feel any gravity,
then it should not radiate.
If not radiating, oscillations wouldn't dampen.
So which one is true, dampen or not dampen ??

DW

That is not "what" the equivalence principle says. Radiation is a far field effect. The field of the electron extends to a global scale. The experiment is intrinsically nonlocal. See section 2 of chapter 7 at
http://www.geocities.com/zcphysicsms/chap7.htm#BM7_2

ardenbook

Can you tell me if it dampen or not dampen ??
If it dampens, then the radiating energy comes from gravity and
shows that gravity is a force.
But in GR, we were taught that gravity is not a force and objects move in geodesic if no other force acts on it.

DW

I thought I did. Yes, it damps. No, gravity is not a real four-vector force. However the spacetime curvature is expressed by a tensor. That is what is real and has real gravitational effects on nonlocal experiments including this one. That level of equivalence is only a statement about local experiments and as such does not apply.