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Casimir—Polder-Like Force for an Atom in Hartle—Hawking Vacuum outside a Schwarzschild Black Hole

We calculate the energy level shift of a static ground state two-level atom interacting with fluctuating massless scalar fields in the Hartle-Hawking vacuum outside a Schwarzschild black hole. It is found that the energy level shift is position-dependent and gives rise to a force on the atom besides the classical gravitational force. This force behaves like r−1(r-2M)−1 for r approaching 2M, whereas it behaves like r−2 for large r.