  We show that without Lorentz invariance, the Unruh effect does not exist. We
use modified dispersion relations and describe in turn: the non-thermal nature
of the vacuum (defined in the preferred frame) restricted to the Rindler wedge,
the loss of the KMS property of the Wigthman function, the transition
amplitudes and transition rates of a uniformaly accelerated detector. This
situation seems to contrast with the Hawking radiation of acoustic black holes,
which under certain assumptions has been shown to be robust to a breaking of
Lorentz symmetry. We explain this discrepancy.
