  An exact solution of the Einstein-Maxwell equations enables us to construct a
hypothesis on the production of tachyons. The hypothesis determines the
kinematical relations for the produced tachyon. It also makes possible to
estimate the empiric conditions necessary for the production. These conditions
can occur when nonpositive subatomic particles of high energy strike atomic
nuclei other than the proton. This suggests how experiments to search for
tachyons can be performed. According to the hypothesis properly designed
experiments with air showers or with the use of the strongest colliders may be
successful. Failure of the air shower experiments performed hitherto is
explained on the grounds of the hypothesis.
