An Electrostatic Analogy for Symmetron Gravity

TL;DR

This paper demonstrates an analogy between symmetron gravity and electrostatics, revealing unique effects like a lightning rod phenomenon and image interactions, which could inform future laboratory tests of modified gravity theories.

Contribution

It introduces a novel electrostatic analogy for symmetron gravity, elucidating its screening mechanism and predicting observable effects such as torque on ellipsoids and field enhancement near pointed objects.

Findings

Symmetron field behaves like electrostatic potential in the quasi-static limit.

Large dense bodies act as perfect conductors, enhancing field gradients at pointed ends.

Symmetron forces include image-like interactions not present in standard gravity.

Abstract

The symmetron model is a scalar-tensor theory of gravity with a screening mechanism that suppresses the effect of the symmetron field at high densities characteristic of the solar system and laboratory scales but allows it to act with gravitational strength at low density on the cosmological scale. We elucidate the screening mechanism by showing that in the quasi-static Newtonian limit there are precise analogies between symmetron gravity and electrostatics for both strong and weak screening. For strong screening we find that large dense bodies behave in a manner analogous to perfect conductors in electrostatics. Based on this analogy we find that the symmetron field exhibits a lightning rod effect wherein the field gradients are enhanced near the ends of pointed or elongated objects. An ellipsoid placed in a uniform symmetron gradient is shown to experience a torque. By symmetry there is no gravitational torque in this case. Hence this effect unmasks the symmetron and might serve as the basis for future laboratory experiments. The symmetron force between a point mass and a large dense body includes a component corresponding to the interaction of the point mass with its image in the larger body. None of these effects have counterparts in the Newtonian limit of Einstein gravity. We discuss the similarities between symmetron gravity and the chameleon model as well as the differences between the two.