Vibrating systems in Schwarzschild spacetime: towards new experiments in gravitation?

TL;DR

This paper investigates how high-frequency vibrations affect a two-body system in Schwarzschild spacetime, revealing significant relativistic effects that differ from Newtonian predictions, with potential experimental implications.

Contribution

It introduces a detailed analysis of vibrational perturbations in relativistic orbital systems, highlighting high-velocity effects and their potential for experimental detection.

Findings

Vibrations induce perturbations near the orbital period.

High velocity effects dominate the amplitude of perturbations.

Significant differences between Newtonian and relativistic predictions are observed at large radii.

Abstract

In this paper the effects of vibrations at high frequencies onto a freely falling two-body system in Schwarzschild spacetime are investigated. As reference motion of the same system without vibrations a circular orbit around the central body is considered. The vibrations induce a perturbation on this motion, whose period is close to the orbital period, in agreement with the simpler situation of the Shirokov effect \cite{Shirokov:1973gr}. In general relativity the amplitude of the perturbation is dominated by high velocity effects, which grow linearly in the radius $r$ of the circular orbit, while the leading term surviving the Newtonian limit decays as $1/r$. Thus even for very large radii a significant difference between Newtonian physics and general relativity is found. We give an estimate of this effect for some molecular vibrations of a system orbiting around the Earth.