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

Why does the Unruh effect rely on Lorentz invariance, while Hawking radiation does not ?