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A remarkable double copy relation of Einstein gravity to QCD in Reggeasymptotics is $\Gamma^{\mu\nu}= \frac12C^\mu C^\nu- \frac12N^\mu N^\nu$, where$\Gamma^{\mu\nu}$ is the gravitational Lipatov vertex in the $2\to 3$ gravitonscattering amplitude, $C^\mu$ its Yang-Mills counterpart, and $N^\mu$ the QEDbremssstrahlung vertex. In QCD, the Lipatov vertex is a fundamental buildingblock of the BFKL equation describing $2\to N$ scattering of gluons at highenergies. Likewise, the gravitational Lipatov vertex is a key ingredient in a2-D effective field theory framework describing trans-Planckian $2\to N$graviton scattering. We construct a quantitative correspondence between asemi-classical Yang-Mills framework for radiation in gluon shockwave collisionsand its counterpart in general relativity. In particular, we demonstrate theLipatov double copy in a dilute-dilute approximation corresponding to$R_{S,L}$, $R_{S,H}$ $ \ll b$, with $R_{S,L}$, $R_{S,H}$ the respectiveemergent Schwarzchild radii generated in shockwave collisions and $b$ is theimpact parameter. We outline extensions of the correspondence developed here tothe dilute-dense computation of gravitational wave radiation in close vicinityof one of the black holes, the construction of graviton propagators in theshockwave background, and a renormalization group approach to compute$2\rightarrow N$ amplitudes that incorporates graviton reggeization andcoherent graviton multiple scattering.

Universal features of $ 2\to N$ scattering in QCD and gravity from shockwave collisions