How the mass of a scalar field influences resonance Casimir-Polder interaction in Schwarzschild spacetime

Resonance Casimir-Polder interaction (RCPI) occurs in nature when two or more atoms are in their excited states and the exchange of a real photon occurs between them due to vacuum fluctuations of the quantum fields. In recent times, many attempts have been made to show that some curved spacetimes can be differentiated from a thermal Minkowski spacetime by using the RCPI. Motivated by these ideas, here we study the RCPI between two atoms that interact with a massive scalar field in Schwarzschild spacetime provided the atoms are placed in the near-horizon region. In this context we use the tool of the open quantum system and calculate the Lamb shift of the atomic energy level of the entangled states. We show that the behavior of RCPI changes depending on the mass of the scalar field. In the high mass limit, the interaction becomes short-ranged and eventually disappears beyond a characteristic length scale of , where m is the mass of the scalar field.