Interaction between two gravitationally polarizable objects induced by thermal bath of gravitons

Abstract

The quadrupole-quadrupole interaction between a pair of gravitationally polarizable objects induced by vacuum fluctuations of the quantum linearized gravitational field is first obtained with a relatively simple method, which is then used to investigate the contribution of thermal fluctuations of a bath of gravitons to the interaction at temperature $T$. Our result shows that, in the high temperature limit, the contribution of thermal fluctuations dominates over that of vacuum fluctuations and the interaction potential behaves like $T/r^{10}$, where $r$ is the separation between the objects, and in the low temperature limit, the contribution of thermal fluctuations is proportional to $T^{10}/r$, which only provides a small correction to the interaction induced by zero-point fluctuations.

11 pages. Accepted by PRD

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• High frequency background gravitational waves from spontaneous emission of gravitons by hydrogen and helium
• Quantum fluctuations of spacetime generate quantum entanglement between gravitationally polarizable subsystems
• Induced quantum gravitational interaction between two objects with permanent quadrupoles in external gravitational fields
• Nonadditive quantum gravitational interaction for three nonpointlike objects
• Quantum gravitomagnetic interaction
• Repulsive quantum gravitoelectric-gravitomagnetic interaction