On elastic deformations of cylindrical bodies under the influence of the gravitational field

Elastic deformations of gravitating cylindrical bodies are relevant for state-of-the-art photonic experiments, as they affect the physical properties of materials under consideration, impacting wave propagation. This is of key importance for a recently planned experiment to explore the influence of the gravitational field on entangled photons propagating in waveguides. The purpose of this work is to determine these elastic deformations as functions of temperature, pressure, and of the gravitational field. We thus determine the deformations of the body due to changes of the gravitational field, and obtain stringent bounds on the control of temperature and pressure so that the effects of the associated elastic deformations on the photons propagating in a waveguide are smaller than the phase shifts associated with the change of the gravitational field.

We use the methods of linear elasticity, including thermoelasticity, to determine the stresses and strains of the medium. For this, the symmetry of the cylinder allows us to solve the problem by using Mitchell's solutions of the equations satisfied by the Airy functions. The boundary conditions are implemented by an approximation of the Hertz contact method.

We calculate the displacements, the stresses and strains for several classes of boundary conditions, and give explicit solutions for a number of physically motivated configurations. The influence of the resulting deformations on the planned GRAVITES experiment is determined.

The results are relevant for fiber interferometry experiments sensitive to the effects of the gravitational field on photon propagation. Our calculations give stringent bounds on the environmental variables, which need to be controlled in such experiments.