Unruh-DeWitt detector response across a Rindler firewall is finite

Abstract

We investigate a two-level Unruh-DeWitt detector coupled to a massless scalar field or its proper time derivative in \((1+1)\)-dimensional Minkowski spacetime, in a quantum state whose correlation structure across the Rindler horizon mimics the stationary aspects of a firewall that Almheiri et al have argued to ensue in an evaporating black hole spacetime. Within first-order perturbation theory, we show that the detector's response on falling through the horizon is sudden but finite. The difference from the Minkowski vacuum response is proportional to \(\omega^{-2}\ln(|\omega|)\) for the non-derivative detector and to \(\ln(|\omega|)\) for the derivative-coupling detector, both in the limit of a large energy gap \(\omega\) and in the limit of adiabatic switching. Adding to the quantum state high Rindler temperature excitations behind the horizon increases the detector's response proportionally to the temperature; this situation has been suggested to model the energetic curtain proposal of Braunstein et al. We speculate that the \((1+1)\)-dimensional derivative-coupling detector may be a good model for a non-derivative detector that crosses a firewall in \(3+1\) dimensions.