Shock Wave Mixing in Einstein and Dilaton Gravity

We consider possible mixing of electromagnetic and gravitational shock waves, in the Planckian energy scattering of point particles in Minkowski space. By boosting a Reissner-Nordstr\"om black hole solution to the velocity of light, it is shown that no mixing of shock waves takes place for arbitrary finite charge carried by the black hole. However, a similar boosting procedure for a charged black hole solution in dilaton gravity yields some mixing : the wave function of even a neutral test particle, acquires a small additional phase factor depending on the dilatonic black hole charge. Possible implications for poles in the amplitudes for the dilaton gravity case are discussed.