Soft zero for cylindrical gravitational waves

TL;DR

This paper demonstrates that cylindrical gravitational waves exhibit a soft zero in their S-matrix, linked to Geroch symmetry, contrasting with the soft pole seen in ordinary gravitons, and indicating no memory effect.

Contribution

It reveals a novel soft zero in the S-matrix for cylindrical gravitational waves, connecting it to Geroch symmetry and highlighting their simplicity.

Findings

Soft zero in cylindrical gravitational wave S-matrix

Connection to Geroch symmetry at infinity

Absence of memory effect in these waves

Abstract

The graviton S-matrix has a famous soft pole. We show that the S-matrix for cylindrical gravitational waves has a soft zero. The soft pole for ordinary gravitons comes from a Ward identity for supertranslation symmetry at asymptotic infinity. We show that the soft zero for cylindrical gravitational waves comes from a Ward identity for Geroch symmetry at asymptotic infinity. Because it is a zero rather than a pole, there is no memory effect. Overall, this soft zero is a manifestation of Geroch symmetry and of the extraordinary simplicity of cylindrical gravitational waves.