  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.
