First Order Corrections to the Unruh Effect

TL;DR

This work analyzes first-order corrections to the Unruh effect for a finite-mass accelerated detector by constructing a first-quantized detector model that includes quantum trajectory smearing and recoil back-reaction. The calculation shows that these effects do not destroy the Unruh effect at leading order, but they induce corrections to the thermal spectrum and to the effective Unruh temperature, yielding a level-dependent $T'_U(n)$ and, in high-energy regimes, a corrected temperature $T_{acc} = T_U\left(1 - T_U/m\right)$. The authors connect these results to black hole physics, deriving corresponding corrections to the Hawking temperature and black hole entropy, and discuss implications for trans-Planckian frequencies in the context of horizon dynamics. Overall, the paper provides a controlled framework to incorporate back-reaction and quantum smearing into Unruh/Hawking phenomena and highlights potential limitations and extensions to quantum gravity regimes.

Abstract

First order corrections to the Unruh effect are calculated from a model of an accelerated particle detector of finite mass. We show that quantum smearing of the trajectory and large recoil essentially do not modify the Unruh effect. Nevertheless, we find corrections to the thermal distribution and to the Unruh temperature. In a certain limit, when the distribution at equilibrium remains exactly thermal, the corrected temperature is found to be $T = T_U( 1 - T_U/M)$, where $T_U$ is the Unruh temperature. We estimate the consequent corrections to the Hawking temperature and the black hole entropy, and comment on the relationship to the problem of trans-planckian frequencies.