QCD-Gravity double-copy in the Regge regime: shock wave propagators

In recent work, we demonstrated a double-copy relation between inclusive gluon radiation in shock wave collisions of ultrarelativistic nuclei and inclusive graviton radiation in trans-Planckian gravitational shock wave collisions. We compute here the corresponding gravitational shock wave propagators in general relativity and demonstrate that they too obey a double copy relation to gluon shock wave propagators computed previously. These results provide key input in a renormalization group approach towards computing the high frequency radiation spectrum in close black hole encounters.