Relativistic Einstein-Podolsky-Rosen Correlations in curved spacetime via Fermi-Walker Transport

Abstract

We present a geometric description to study the relativistic EPR correlations in curved spacetime background given by the application of the Fermi-Walker transport in the relativistic EPR states and we show that its result has the same effect as the applications of successive infinitesimal Lorentz boosts in the relativistic EPR states. We also show that the expression for the Bell inequality due to the Fermi-Walker transport is equivalent to the expression demonstrated by Terashima and Ueda \cite{TU2}, where the degree of violation of the Bell inequality is dependent of the angle of the Wigner rotation. This geometrical approach to study the relativistic EPR correlations is a promissing formulation to investigate the EPR correlations in the general relativity background.