Directional dependence of the Unruh effect for spatially extended detectors

Abstract

We analyse the response of a spatially extended direction-dependent local quantum system, a detector, moving on the Rindler trajectory of uniform linear acceleration in Minkowski spacetime, and coupled linearly to a quantum scalar field. We consider two spatial profiles: (i) a profile defined in the Fermi-Walker frame of an arbitrarily-accelerating trajectory, generalising the isotropic Lorentz-function profile introduced by Schlicht to include directional dependence; and (ii) a profile defined only for a Rindler trajectory, utilising the associated frame, and confined to a Rindler wedge, but again allowing arbitrary directional dependence. For (i), we find that the transition rate on a Rindler trajectory is non-thermal, and dependent on the direction, but thermality is restored in the low and high frequency regimes, with a direction-dependent temperature, and also in the regime of high acceleration compared with the detector's inverse size. For (ii), the transition rate is isotropic, and thermal in the usual Unruh temperature. We attribute the non-thermality and anisotropy found in (i) to the leaking of the Lorentz-function profile past the Rindler horizon. * sanved.kolekar@cbs.ac.in

Quantum kicks near a Cauchy horizon

“…This will make the coupling between the field and the detector slightly singular, but the singularity will not produce infinities in the first-order perturbative treatment that we shall follow below. Allowing the detector to have a nonzero spatial size, as in the detector model originally introduced by Unruh, 20 would present a technical challenge for formulating the notion of a spatial profile when the spacetime is curved, or even in flat spacetime when the detector's motion is non-inertial; 22,23,[34][35][36] further, a finite spatial size would raise questions about the relativistic consistency of the coupled system, and about the sense in which the two-level detector approximates an underlying more fundamental detection described by quantum fields. [37][38][39][40] For the localization in time, we assume that the detector operates for a finite interval of proper time.…”