Particle detector in a position-superposed black hole spacetime

TL;DR

This paper investigates how an Unruh--DeWitt detector responds in a superposed black hole spacetime, revealing nonclassical measurement outcomes and differences from classical mixtures.

Contribution

It introduces a method to analyze detector responses in superposed black hole spacetimes and compares results with previous mass-superposition studies.

Findings

Detection probabilities include nonclassical contributions absent in classical mixtures.

Analytical derivation shows differences from mass-superposed black holes due to spectral singularities.

The approach extends understanding of quantum effects in superposed gravitational fields.

Abstract

We calculate the response of an Unruh--DeWitt detector in a 2+1d spacetime that contains a BTZ black hole in a superposition of locations. Upon performing a Quantum Reference Frame (QRF) transformation, this can also be seen as a detector in a superposition of locations in a single classical black hole spacetime. We use this to derive the form of the interaction of the detector and scalar field in such a superposition of spacetimes, ignoring backreaction. We define a measurement whose outcome probabilities contain a nonclassical contribution that would be absent for a black hole described by a classical mixture of positions. Finally, we compare our results with a previously studied setup involving a mass-superposed black hole by Foo et al in [Phys. Rev. Lett. 129, 181301 (2022)], and highlight a key difference. We show analytically how this difference arises from singularities in the spectrum probed by the detector.