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

Abstract

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 \emph{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 \emph{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 \emph{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.

17 pages