Remarks on distinguishability of Schwarzschild spacetime and thermal Minkowski spacetime using Resonance Casimir-Polder interaction

One perceives same response of a single-atom detector when placed at a point outside the horizon in Schwarzschild spacetime to that of a static single-atom detector in thermal Minkowski spacetime. So one cannot distinguish Schwarzschild spacetime from thermal Minkowski spacetime by using a single-atom detector. We show that, for Schwarzschild spacetime, beyond a characteristic length scale which is proportional to the inverse of the surface gravity kappa, the Resonance Casimir-Polder interaction (RCPI) between two entangled atoms is characterized by a 1/L-2 power-law provided the atoms are located close to the horizon. However, the RCPI between two entangled atoms follows a 1/L power-law decay for the thermal Minkowski spacetime. Seemingly, it appears that the spacetimes can be distinguished from each other using the RCPI behavior. But our further exploration leads to the conclusion that the length scale limit beyond a characteristic value is not compatible with the local flatness of the spacetime.