Theory predicts that uniform acceleration leads to experiencing thermal radiation (so called Fulling Davies Unruh radiation), associated with the appearance of an event horizon. For non uniform but unidirectional acceleration the shape of the experienced radiation changes from thermal to other spectral densities, but also is predicted to exist. But suppose the acceleration is periodic and oscillatory, i.e. no permanent horizon persists? In particular, what about the case of harmonic motion, for a full cycle, half a cycle, etc.?
Here is an even simpler related problem that makes the apparent paradox easier to see. Suppose at proper time t=0, I accelerate at constant acceleration k in the x direction for t0 seconds, presumably experiencing Unruh radiation. Then I accelerate with acceleration -k, (in the -x direction,) for 2*t0 seconds, seeing more Unruh radiation coming from the opposite direction, and then I finish with with acceleration +k for the final t0 seconds. At the end of the 4*t0 proper seconds, I'm back where I started, at rest, without any event horizon. Was the Unruh radiation I felt when reversing acceleration secretly correlated or entangled with the radiation I initially and finally saw? Otherwise, from a more macro scale, I didn't actually necessarily move much, and the acceleration event horizon was instantaneous, evanescent and fleeting, so whence arose the Unruh radiation?