The EPR correlation in Kerr-Newman spacetime Jackson Levi Said 1 and Kristian Zarb Adami 1, 2 $^{1}$Physics Department, University of Malta, Msida, Malta $^{2}$Physics Department, University of Oxford, Oxford, OX1 3RH, United Kingdom (Dated: 29th November 2009) The EPR correlation has become an integral part of quantum communications as has general relativity in classical communication theory, however when combined an apparent deterioration is observed for spin states. We consider appropriate changes in directions of measurement to exploit full EPR entanglement for a pair of particles and show that it can be deduced only up to the outer even horizon of a Kerr-Newman black hole, even in the case of freely falling observer. PACS numbers: 97.60.Lf.-s For some of the founders of quantum mechan- ics one of the troubling parts was the spooky action-at-a-distance. Originally this was thought up by Einstein-Podolsky-Rosen (EPR) in an at- tempt to challenge certain aspects of quantum theory at the time. Contrary to its original de- sign it is now the cornerstone of modern main- stream quantum physics, from cryptography to quantum computation, thus it is important to understand as many of the properties of quan- tum communications as possible. In particular it is of importance to fully understand the ef- fect of spacetime curvature on EPR states. This is completely different from classical information transport. In this scenario the space between ob- server and emitter does not have an effect on the transmission which means that only local space- time effects matter when making measurements on transmissions. In this paper, we apply the Terashima and Ueda [1] approach to the spacetime background of a Kerr-Newman black hole. In general relativity the spin of a particle becomes deformed in all but the Minkowski spacetime. We present a method to extract the complete EPR correlation of two particles in a Bell state in Kerr-Newman geome- try, ignoring helicity of infalling particles. These particles are defined locally and so suffer a preces- sion of their spin component due an acceleration by an external force and the difference in the local inertial frame at different points about the given geometry. Taking these differences to arise from a continuous succession of local Lorentz transfor- mations (LLT), the spin component can be calcu- The most general vacuum solution of Einstein’s field equations for black holes is the Kerr- Newman metric, any further complications re- quires one to consider hairy black holes. In this paper we take the Minkowski signature to be η = diag( − , + , + , +) and use geometric units ( G = 1 = c ). Latin letters are run over the four inertial labels (0,1,2,3) and Greek letters over the four general coordinate labels. Also repeated indices are to be summed. Then the metric for the Kerr-Newman spacetime in Boyer- Lindquist coordinates ( t, r, θ, φ ) for an observer at infinity is given by This paper is organized as follows, in Sec. II we derive the spin precession in the Kerr-Newman background for an observer at infinity. Then in Sec. III we consider the EPR correlation for a pair of fully entangled particles. In an attempt to remove the coordinate singularities from the derived angle we then calculate the spin preces- sion for an infalling observer in Sec. IV. In Sec. V we discuss Bell’s inequality for the observers at infinity and the infalling observer. Finally in Sec. VI we summarize our results. lated since it precesses in accord with the Wigner rotation. It is therefore not a trivial task to de- scribe the motion of a particle using quantum mechanics near a Kerr-Newman black hole be- cause the Poincar´ e group does not act intuitively in this region. I. INTRODUCTION II. KERR-NEWMAN DISTORTION arXiv:1001.0788v3 [quant-ph] 23 Jun 2010