An Electrostatic Analogy for Symmetron Gravity
  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.
