Fulling–Davies–Unruh effect with non-uniform acceleration

Question

Can there be some version of the Fulling–Davies–Unruh effect, in which the accelerating observer is moving with a non-uniform acceleration? Can someone refer some papers to read?

If there can not be such a version of the effect under consideration and we can say that with certainty, which is the reason?

Any help will be appreciated.

Answer 1

I see two possible, reasonable, and interesting interpretations for this question. I'll answer both of them. I'll start with the easier one, and then move on to the hardest.

Can a non-uniformly accelerating observer perceive the Minkowski vacuum as having particles?

I'm pretty sure the answer is yes. The notion of particle is extremely observer-dependent and it would be actually surprising if they were to agree with an inertial observer without being inertial themself. Deep down, the notion of particle is related to the observer's notion of what is positive energy, which is then related to the observer's worldline (see this answer I wrote a while ago). If they have different notions of what is positive energy, they will have different notions of particle. I would find it surprising for a non-inertial observer to actually see no particles in the Minkowski vacuum.

Can a non-uniformly accelerating observer perceive the Minkowski vacuum as being thermal?

This requires the observer to not only see particles, but also for them to obey a thermal spectrum. That's a lot more difficult. I find it unlikely, because the thermal spectrum is related to the observers moving along the orbits of a timelike Killing field in the spacetime. Namely, accelerating observers move along wordlines composed of events related by Lorentz boosts. This symmetry is related to the occurrence of a thermal spectrum (a 1991 paper by Kay and Wald discusses how the existence of such a symmetry ends up leading to a thermal spectrum). In the Minkowski spacetime, there are ten independent Killing fields (the maximum possible). The possible symmetries we could then exploit would be:

• timelike translation: this is the usual notion of time and inertial observers move along these lines,
• 3 boosts: in the regions in which they are timelike, these correspond to uniformly accelerated observers moving toward different directions;
• 3 spacelike translations: these are spacelike and no observer can move along them;
• 3 rotations: these are spacelike and no observer can move along them.

Hence, there are no other available symmetries left, which means it seems unlikely for other observables to also experience thermality. Furthermore, this lack of symmetry can make the analysis somewhat more challenging, which explains why there is such a huge focus on uniform acceleration.