Response of finite-time particle detectors in non-inertial frames and curved spacetime

TL;DR

This paper investigates how finite-time particle detectors respond in non-inertial and curved spacetimes, revealing transient effects, dependence on switching functions, and detailed responses in various spacetime geometries.

Contribution

It provides a general formula for finite-time detector response with arbitrary switching functions and analyzes the effects in Minkowski, Schwarzschild, and de-Sitter spacetimes.

Findings

Detectors respond even on inertial trajectories due to transients.

Response depends on the switching function's nature and duration.

Detailed response formulas for Gaussian and exponential window functions.

Abstract

The response of the Unruh-DeWitt type monopole detectors which were coupled to the quantum field only for a finite proper time interval is studied for inertial and accelerated trajectories, in the Minkowski vacuum in (3+1) dimensions. Such a detector will respond even while on an inertial trajctory due to the transient effects. Further the response will also depend on the manner in which the detector is switched on and off. We consider the response in the case of smooth as well as abrupt switching of the detector. The former case is achieved with the aid of smooth window functions whose width, $T$, determines the effective time scale for which the detector is coupled to the field. We obtain a general formula for the response of the detector when a window function is specified, and work out the response in detail for the case of gaussian and exponential window functions. A detailed discussion of both $T \rightarrow 0$ and $T \rightarrow \infty$ limits are given and several subtlities in the limiting procedure are clarified. The analysis is extended for detector responses in Schwarzschild and de-Sitter spacetimes in (1+1) dimensions.