Frequency spectrum of an optical resonator in a curved spacetime

TL;DR

This paper analyzes how gravity and acceleration affect the frequency spectrum of optical resonators in curved spacetime, deriving explicit formulas and exploring implications for relativistic rigidity and practical systems.

Contribution

It provides explicit expressions for the frequency spectrum perturbations of optical resonators in curved spacetime, considering both rigid and deformable models, including relativistic effects.

Findings

Frequency spectrum perturbation depends on the speed of sound in the resonator.

Relativistic rigidity is connected to the speed of sound approaching the speed of light.

Results apply to systems in strong gravitational fields, including near black holes.

Abstract

The effect of gravity and proper acceleration on the frequency spectrum of an optical resonator - both rigid or deformable - is considered in the framework of general relativity. The optical resonator is modeled either as a rod of matter connecting two mirrors or as a dielectric rod whose ends function as mirrors. Explicit expressions for the frequency spectrum are derived for the case that it is only perturbed slightly. For a deformable resonator, the perturbation of the frequency spectrum depends on the speed of sound in the rod supporting the mirrors. A connection is found to a relativistic concept of rigidity when the speed of sound approaches the speed of light. In contrast, the corresponding result for the assumption of Born rigidity is recovered when the speed of sound becomes infinite. The results presented in this article can be used as the basis for the description of optical and opto-mechanical systems in a curved spacetime. We apply our results to the examples of a uniformly accelerating resonator and an optical resonator in the gravitational field of a small moving sphere. Our approach is not limited to weak gravitational fields, which we exemplify by its application to the fictitious situation of an optical resonator falling into a black hole.