We propose a method by which one could use modified antimatter gravity experiments
in order to perform a high-precision test of antimatter charge neutrality. The proposal
is based on the application of a strong, external, vertically oriented electric field
during an antimatter free-fall gravity experiment in the gravitational field of the
Earth. The proposed experimental setup has the potential to drastically improve the
limits on the charge-asymmetry parameter (epsilon) over bar (q) of antimatter. On
the theoretical side, we analyze possibilities to describe a putative charge-asymmetry
of matter and antimatter, proportional to the parameters epsilon(q) and (epsilon)
over bar (q), by Lagrangian methods. We found that such an asymmetry could be described
by four-dimensional Lorentz-invariant operators that break CPT without destroying
the locality of the field theory. The mechanism involves an interaction Lagrangian
with field operators decomposed into particle or antiparticle field contributions.
Our Lagrangian is otherwise Lorentz, as well as PT invariant. Constraints to be derived
on the parameter (epsilon) over bar (q) do not depend on the assumed theoretical model.