Response of an Unruh-DeWitt detector near an extremal black hole

TL;DR

This paper analyzes how an Unruh-DeWitt detector responds near an extremal black hole, using the Bertotti-Robinson spacetime to obtain explicit two-point functions and studying effects like thermalization and anti-Unruh phenomena.

Contribution

It provides a detailed analysis of the detector's response in extremal black hole backgrounds, including explicit calculations in the Bertotti-Robinson spacetime for various quantum states.

Findings

Detector exhibits thermalization in different quantum states.

Anti-Unruh and anti-Hawking effects are observed.

Explicit response functions are derived for the near-horizon region.

Abstract

We consider the response of an Unruh-DeWitt detector near an extremal charged black hole, modeling the near-horizon region of this extremal spacetime by the Bertotti-Robinson spacetime. The advantage of employing the Bertotti-Robinson limit is that the two-point functions for a massless scalar field are obtainable in closed form for the field in a number of quantum states of interest. We consider the detector coupled to a massless field in both the Boulware vacuum state and arbitrary thermal states, including the Hartle-Hawking state, and analyse the detector's response for a broad range of trajectories. Particular attention is paid to the thermalization of the detector, the anti-Unruh and anti-Hawking effect.