Unruh-DeWitt detector on the BTZ black hole

TL;DR

This paper investigates how an Unruh-DeWitt detector interacts with a scalar field near a BTZ black hole, revealing thermal responses for co-rotating detectors and non-thermal responses for free-falling detectors, influenced by boundary conditions.

Contribution

It provides a causal, regular expression for the detector's transition rate in curved spacetime and analyzes its behavior in the BTZ black hole background with different detector motions.

Findings

Co-rotating detector responds thermally at Hawking temperature.

Freely-falling detector shows no thermality near the horizon.

Boundary conditions at infinity significantly affect transition rates.

Abstract

We examine an Unruh-DeWitt particle detector coupled to a scalar field in three-dimensional curved spacetime, within first-order perturbation theory. We first obtain a causal and manifestly regular expression for the instantaneous transition rate in an arbitrary Hadamard state. We then specialise to the Ba\~nados-Teitelboim-Zanelli black hole and to a massless conformally coupled field in the Hartle-Hawking vacuum. A co-rotating detector responds thermally in the expected local Hawking temperature, while a freely-falling detector shows no evidence of thermality in regimes that we are able to probe, not even far from the horizon. The boundary condition at the asymptotically anti-de Sitter infinity has a significant effect on the transition rate.