  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.
