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

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.