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 showers experiments performed hitherto is explained on the grounds of the hypothesis.

PACS numbers: 14.80.Kx, 25.90.+k