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

## TL;DR

This paper derives how thermal graviton fluctuations influence the quadrupole-quadrupole interaction between gravitationally polarizable objects, showing dominance at high temperatures and minor effects at low temperatures.

## Contribution

It introduces a simple method to calculate thermal graviton effects on gravitational interactions, extending previous vacuum fluctuation analyses.

## Key findings

- Thermal fluctuations dominate at high temperatures with a $T/r^{10}$ dependence.
- At low temperatures, thermal effects are proportional to $T^{10}/r$, acting as small corrections.
- The interaction behavior varies significantly between high and low temperature regimes.

## 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.