Chameleon gravity, electrostatics, and kinematics in the outer galaxy

Light scalar fields are expected to arise in theories of high energy physics (such as string theory), and find phenomenological motivations in dark energy, dark matter, or neutrino physics. However, the coupling of light scalar fields to ordinary (or dark) matter is strongly constrained from laboratory, solar system, and astrophysical tests of the fifth force. One way to evade these constraints in dense environments is through the chameleon mechanism, where the field's mass steeply increases with ambient density. Consequently, the chameleonic force is only sourced by a thin shell near the surface of dense objects, which significantly reduces its magnitude. In this paper, we argue that thin-shell conditions are equivalent to conducting boundary conditions in electrostatics. As an application, we use the analogue of the method of images to calculate the back-reaction (or self-force) of an object around a spherical gravitational source. Using this method, we can explicitly compute the violation of the equivalence principle in the outskirts of galactic haloes (assuming an NFW dark matter profile): Intermediate mass satellites can be slower than their larger/smaller counterparts by as much as 10% close to a thin shell.