The far-zone interatomic Casimir-Polder potential between two ground-state atoms outside a Schwarzschild black hole

Based on the idea that the vacuum fluctuations of electromagnetic fields can induce instantaneous correlated dipoles, we study the far-zone Casimir-Polder potential between two atoms in the Boulware, Unruh and Hartle-Hawking vacua outside a Schwarzschild black hole. We show that, at spatial infinity, the Casimir-Polder potential in the Boulware vacuum is similar to that in the Minkowski vacuum in flat spacetime with a behavior of $R^{-7}$, so is in the Unruh vacuum as a result of the backscattering of the Hawking radiation from the black hole off the spacetime curvature. However, the interatomic Casimir-Polder potential in the Hartle-Hawking vacuum behaves like that in a thermal bath at the Hawking temperature. In the region near the event horizon of the black hole, the modifications caused by the space-time curvature make the interatomic Casimir-Polder potential smaller in all three vacuum states.