# Thermal and nonthermal scaling of the Casimir-Polder interaction in a black hole spacetime

## TL;DR

This paper investigates how the Casimir-Polder force between two atoms near a black hole transitions from thermal-like to nonthermal behavior depending on their proximity to the event horizon, influenced by Hawking radiation.

## Contribution

It reveals the scaling transition of the Casimir-Polder interaction in a black hole spacetime and compares it with accelerated frame effects, considering different quantum field vacua.

## Key findings

- Transition from thermal to nonthermal Casimir-Polder scaling near the horizon
- Crossover length scale related to black hole surface gravity and atomic acceleration
- Consistent behavior across Boulware, Hartle-Hawking, and Unruh vacua

## Abstract

We study the Casimir-Polder force arising between two identical two-level atoms and mediated by a massless scalar field propagating in a black-hole background. We study the interplay of Hawking radiation and Casimir-Polder forces and find that, when the atoms are placed near the event horizon, the scaling of the Casimir-Polder interaction energy as a function of interatomic distance displays a transition from a thermallike character to a nonthermal behavior. We corroborate our findings for a quantum field prepared in the Boulware, Hartle-Hawking, and Unruh vacua. Our analysis is consistent with the nonthermal character of the Casimir-Polder interaction of two-level atoms in a relativistic accelerated frame [J. Marino et al., Phys. Rev. Lett. 113, 020403 (2014)], where a crossover from thermal scaling, consistent with the Unruh effect, to a nonthermal scaling has been observed. The two crossovers are a consequence of the noninertial character of the background where the field mediating the Casimir interaction propagates. While in the former case the characteristic crossover length scale is proportional to the inverse of the surface gravity of the black hole, in the latter it is determined by the inverse of the proper acceleration of the atoms.