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We study the relationship between shockwave geometries and the gravitational
memory effect in four-dimensional asymptotically flat spacetime. In particular,
we show the 't Hooft commutation relations of shockwave operators are
equivalent to the commutation relation between soft and Goldstone modes
parametrizing a sector of the gravitational phase space. We demonstrate this
equivalence via a diffeomorphism that takes the shockwave metric to a metric
whose transverse traceless component is the gravitational memory. The shockwave
momentum in 't Hooft's analysis is related to the soft graviton mode, which is
responsible for the memory effect, while the shift in the shockwave position is
related to the Goldstone mode. This equivalence opens new directions to utilize
the gravitational memory effect to explore the observational implications of
shockwave geometries in flat space.
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