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Soft vanishing of the scattering amplitudes for cylindrical gravitational waves

Robert Penna*

  • *Contact author: pennar@sunypoly.edu
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Phys. Rev. D 112, 046002 – Published 5 August, 2025

DOI: https://doi.org/10.1103/28x6-7d9p

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.

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Phys. Rev. D 112, 046002– Published 5 August, 2025
  • Received 4 June 2024
  • Revised 16 July 2024
  • Accepted 17 July 2025
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