Shock Wave Mixing in Einstein and Dilaton Gravity

TL;DR

This paper investigates the interaction of electromagnetic and gravitational shock waves during high-energy particle scattering, revealing no mixing in Einstein gravity but some mixing in dilaton gravity due to black hole charge effects.

Contribution

It demonstrates that electromagnetic and gravitational shock wave mixing does not occur in Einstein gravity but can occur in dilaton gravity, highlighting the role of black hole charge.

Findings

No shock wave mixing in Einstein gravity with charged black holes.

Shock wave mixing occurs in dilaton gravity due to black hole charge.

Dilaton black holes induce phase shifts in test particles.

Abstract

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.