Quantum entanglement in Plebański-Demiański spacetimes

For an Einstein–Podolsky–Rosen pair of spin-1/2 particles in circular orbits in a general axially symmetric spacetime, the spin precession angle is obtained. Hovering observers are introduced for ensuring fixed reference frames to perform suitable reliable measurements. Frame-dragging of spinning holes is explicitly incorporated relative to hovering observers. The spin-singlet state is found to be mixed with the spin-triplet by acceleration and gravity effects, which deteriorate the perfect anti-correlation of an entangled pair of spins measured by hovering observers. Finally, an algorithm to calculate spin precession for a general axially symmetric spacetime is proposed. This algorithm is applied to study the complete list of expanding and twisting Type-D Plebaski–Demiaski black holes and their descendent limiting solutions with lower parameters. PACS numbers: 03.65.Ud, 03.67.−a, 04.20.−q, 02.40.−k (Some figures may appear in colour only in the online journal)