Comment on "Background thermal contributions in testing the Unruh effect"

Costa and Matsas (gr-qc/9412030) claimed in their recent paper that a thermal bath does not affect substantially the transition probability for fast moving inertial Unruh detector. It is shown that their claim holds only for small $βΔE$. We show that, for large enough $βΔE$, the transition probability is not monotonically decreasing function of the detector's speed contrary to their claim.

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