  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.
