Induced quantum gravitational interaction between two objects with permanent quadrupoles in external gravitational fields

TL;DR

This paper explores how external gravitational radiation influences quantum gravitational interactions between objects with permanent quadrupoles, revealing new effects when objects are polar and the radiation wavelength is large.

Contribution

It introduces a quantum gravity model for polar objects with quadrupoles under external gravitational fields, highlighting an additional interaction term not present in nonpolar cases.

Findings

Additional interaction term exists for polar objects due to graviton scattering.

Interaction differs significantly for polar objects at small distances compared to nonpolar ones.

Model can be extended to stochastic gravitational backgrounds.

Abstract

We investigate, in the framework of linearized quantum gravity, the induced quantum gravitational interaction between two ground-state objects with permanent quadrupole moments, which are subjected to an external gravitational radiation field. Compared with the nonpolar case, there exists an additional term in the leading-order field-induced interobject interaction between two polar objects. This term arises when a real graviton is scattered by the same object center with coupling between the two objects occurring via the exchange of a single virtual graviton, and the interaction is thus relevant to the number density of gravitons, the frequency and polarization of the external gravitational field, as well as the permanent quadrupoles of the objects. Due to the existence of such an additional term, the field-induced quantum gravitational interaction between two polar objects can be significantly different from that between nonpolar ones when the interobject distance is much smaller than the wavelength of the external gravitational radiation field. Although we model the external gravitational radiation as a quantized monochromatic gravitational wave with a certain wave vector and polarization for simplicity, it is possible to generalize to more realistic situations, such as the case of a stochastic background of gravitational radiation.