Modified dispersion relations and the response of the rotating Unruh-DeWitt detector

TL;DR

This paper investigates the response of a rotating Unruh-DeWitt detector coupled to a scalar field with non-linear dispersion relations, showing that the response can be numerically computed exactly and is affected differently by super-luminal and sub-luminal modifications.

Contribution

It demonstrates that the response of a rotating detector with non-linear dispersion relations can be exactly numerically computed, unlike the accelerated case, and explores boundary effects.

Findings

Response can be computed exactly via numerical methods.

Super-luminal dispersion relations have minimal impact.

Sub-luminal relations cause significant modifications.

Abstract

We study the response of a rotating monopole detector that is coupled to a massless scalar field which is described by a non-linear dispersion relation in flat spacetime. Since it does not seem to be possible to evaluate the response of the rotating detector analytically, we resort to numerical computations. Interestingly, unlike the case of the uniformly accelerated detector that has been considered recently, we find that defining the transition probability rate of the rotating detector poses no difficulties. Further, we show that the response of the rotating detector can be computed {\it exactly}\vee (albeit, numerically) even when it is coupled to a field that is governed by a non-linear dispersion relation. We also discuss the response of the rotating detector in the presence of a cylindrical boundary on which the scalar field is constrained to vanish. While super-luminal dispersion relations hardly affect the standard results, we find that sub-luminal dispersion relations can lead to relatively large modifications.