  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 ${\overline \epsilon}_q$ 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 ${\overline \epsilon}_q$, 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 ${\overline \epsilon}_q$ do not depend on the assumed theoretical
model.
