How to kill the Unruh effect

TL;DR

This paper demonstrates that enforcing continuity in the Rindler transformation as acceleration approaches zero eliminates the Unruh effect for a massive scalar field by restricting mode expansion to positive energies.

Contribution

It introduces a continuity condition on the Rindler transformation that removes the Unruh effect by limiting the mode spectrum to positive energies.

Findings

Unruh effect disappears under the continuity condition

The restriction to positive energy spectrum suppresses Bogoliubov beta terms

Continuity of Rindler transformation is key to eliminating the effect

Abstract

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.