  How to kill the Unruh effect? Very simple, by requiring the Rindler
transformation to behave continuously for vanishing acceleration. Then the
Unruh effect disappears as we show in the case of the massive scalar quantum
field. The main point is that the continuity condition restricts the integral
of the mode expansion to the positive energy spectrum, suppressing thus the
$\beta$ - terms of the Bogoliubov transformation.
