Casimir-Polder-like force on an atom outside a Schwarzschild black hole

TL;DR

This paper investigates the position-dependent quantum forces on an atom outside a black hole, revealing attractive and repulsive behaviors influenced by vacuum states and Hawking radiation.

Contribution

It introduces a quantum field theoretical calculation of atom-black hole interactions, highlighting new force behaviors in different vacuum states.

Findings

Force is attractive near the horizon in Boulware vacuum.

Force is repulsive far from the black hole in Boulware vacuum.

Hawking radiation causes a divergent attractive force at the horizon in Unruh vacuum.

Abstract

We calculate, in the framework of open quantum systems, the ground state energy-level shift for a static two-level atom outside a spherically symmetric black hole in interaction with fluctuating massless scalar fields in the Boulware and Unruh vacuums. We find that the energy-level shift is position-dependent and thus gives rise to a force on the atom besides the classical gravitational force. For the case of the Boulware vacuum which represents a star that has not collapsed through its event horizon, this force is attractive near the horizon and is repulsive far away from the black hole with a behavior of $r^{-3}$ . For the case of the Unruh vacuum which represents a radiating black hole, we find that the contribution to the Casimir-Polder-like force due to the presence of Hawking radiation is always attractive and, remarkably, this attractive force diverges at the event horizon.