Acceleration has no effect on a causality-enforcing trivial vacuum, so the Unruh effect is absent and standard calculations omit a cancelling contribution from Lorentz transformations acting on the detector.
Finite-temperature field theory; Cambridge University Press, Cambridge UK, 1989
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Poincar\'e invariance and the Unruh effect
Acceleration has no effect on a causality-enforcing trivial vacuum, so the Unruh effect is absent and standard calculations omit a cancelling contribution from Lorentz transformations acting on the detector.