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

TL;DR

The paper investigates how the resonance Casimir-Polder interaction between entangled atoms can distinguish Schwarzschild spacetime from thermal Minkowski spacetime, revealing differences in interaction decay laws near the horizon.

Contribution

It demonstrates that RCPI behavior differs between the two spacetimes and clarifies the limitations of using this difference for spacetime distinguishability.

Findings

RCPI follows a 1/L^2 decay near the horizon in Schwarzschild spacetime.

RCPI follows a 1/L decay in thermal Minkowski spacetime.

Beyond a certain length scale, spacetime flatness constraints invalidate the distinguishability.

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.