Nonadditive quantum gravitational interaction for three nonpointlike objects

We explore the nonadditive three-body quantum gravitational quadrupole interaction among three nonpointlike objects in their ground states in the framework of linearized quantum gravity and find that the interaction exhibits a distance behavior of $r_A^{-5}r_B^{-5}r_C^{-5}$ in the near regime where the interobject distances are small compared with the characteristic transition wavelength of the objects, and $r_A^{-5}r_B^{-5}r_C^{-5}(r_A+r_B+r_C)^{-1}$ in the far regime where the distances are larger than the characteristic transition wavelength, where $r_\xi$ denotes the distance between any two objects except object $\xi\;(\xi=A,B,C)$. Compared to the additive quantum gravitational interaction between two ground-state objects in vacuum which is always attractive both in the near and far regimes, the nonadditive interaction among three ground-state objects can be either attractive or repulsive depending on the geometrical configuration of these objects. That is, in principle, the attractive or repulsive properties of the nonadditive three-body quantum gravitational interaction can be manipulated by changing the geometrical arrangement of the objects.