Quantum interaction between two gravitationally polarizable objects in presence of boundaries

TL;DR

This paper studies how boundaries affect quantum gravitational interactions between polarizable objects, revealing that boundaries can enhance and alter the interaction depending on boundary type and object orientation.

Contribution

It provides the first analysis of boundary effects on quantum gravitational interactions, showing how different boundary conditions influence the interaction strength and dependence on separation.

Findings

Boundaries always strengthen the interaction compared to no-boundary case.

Neumann boundary enhances interaction more when objects are parallel to it.

Dirichlet boundary results in larger interaction when objects are perpendicular to it.

Abstract

We investigate, in the framework of the linearized quantum gravity and the leading-order perturbation theory, the quantum correction to the classical Newtonian interaction between a pair of gravitationally polarizable objects in the presence of both Neumann and Dirichlet boundaries. We obtain general results for the interaction potential and find that the presence of a boundary always strengthens in the leading-order the interaction as compared with the case in absence of boundaries. But different boundaries yield a different degree of strengthening. In the limit when one partner of the pair is placed very close to the Neumann boundary, the interaction potential is larger when the pair is parallel with the boundary than when it is perpendicular to, which is just opposite to the case when the boundary is Dirichlet where the latter is larger than the former. In addition, we find that the pair-boundary separation dependence of the higher-order correction term is determined by the orientation of the pair with respect to boundary, with the parallel case giving a quadratic behavior and the perpendicular case a linear one.