Quantum interaction between two entangled non point-like objects in the presence of boundaries

Abstract

We explore, in the framework of linearized quantum gravity, the quantum gravitational quadrupole-quadrupole interaction between two entangled non point-like objects in the presence of both Dirichlet and Neumann boundaries. The results show that, compared to the case without boundaries, the interaction can be either enhanced or weakened depending on the geometrical arrangement of the objects with respect to the boundaries. In the limit when the two-object system is placed very close to the Dirichlet boundary, the near-regime interaction potential is larger than that of the pure vacuum case when the two objects are placed perpendicular to the boundary but smaller when parallel to it, while, in the far regime, such strong and weak relations between potentials are just opposite to that in the near regime. And, there exists a new $r^{-2}$ far-regime behavior of the interaction potential under the perpendicular configuration. For the case of Neumann boundary, the strong and weak relations between the interaction potentials under perpendicular or parallel configurations and the case without boundary are opposite to the Dirichlet circumstance both in the near and far regimes. Besides, the novel $r^{-2}$ far-regime behavior occurs for the parallel rather than perpendicular configuration in the presence of Neumann boundary.