# The Unruh Effect for Eccentric Uniformly Rotating Observers

## TL;DR

This paper investigates the Unruh effect for eccentric uniformly rotating observers using relativistic rotational transformations, revealing non-zero detector responses and challenges in canonical vacuum definitions, thus questioning previous assumptions based on Galilean transformations.

## Contribution

It introduces relativistic rotational transformations for eccentric observers to study the Unruh effect, showing non-zero detector responses and issues with canonical vacuum states.

## Key findings

- Detector response function is non-zero for eccentric rotating observers.
- Canonical particle number expectation value can be zero with modified Franklin transformation.
- The correspondence between vacuum states and detector responses is broken for rotating observers.

## Abstract

It is common to use Galilean rotational transformation to investigate the Unruh effect for uniformly rotating observers. However, the rotating observer in this subject is an eccentric observer while Galilean rotational transformation is only valid for centrally rotating observers. Thus, the reliability of the results of applying Galilean rotational transformation to the study of the Unruh effect might be considered as questionable. In this work the rotational analog of the Unruh effect is investigated by employing two relativistic rotational transformations corresponding to the eccentric rotating observer, and it is shown that in both cases the detector response function is non-zero. It is also shown that although consecutive Lorentz transformations can not give a frame within which the canonical construction can be carried out, the expectation value of particle number operator in canonical approach will be zero if we use modified Franklin transformation. These conclusions reinforce the claim that correspondence between vacuum states defined via canonical field theory and a detector is broken for rotating observers. Some previous conclusions are commented on and some controversies are also discussed.