On BMS Invariance of Gravitational Scattering

Dec 8, 2013
20 pages
Published in:
  • JHEP 07 (2014) 152
  • Published: 2014
e-Print:

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Abstract: (arXiv)
BMS+ transformations act nontrivially on outgoing gravitational scattering data while preserving intrinsic structure at future null infinity (I+). BMS- transformations similarly act on ingoing data at past null infinity (I-). In this paper we apply - within a suitable finite neighborhood of the Minkowski vacuum - results of Christodoulou and Klainerman to link I+ to I- and thereby identify "diagonal" elements BMS0 of (BMS+)X(BMS-). We argue that BMS0 is a nontrivial infinite-dimensional symmetry of both classical gravitational scattering and the quantum gravity S-matrix. It implies the conservation of net accumulated energy flux at every angle on the conformal S2 at I+. The associated Ward identity is shown to relate S-matrix elements with and without soft gravitons. Finally, BMS0 is recast as a U(1) Kac-Moody symmetry and an expression for the Kac-Moody current is given in terms of a certain soft graviton operator on the boundary of null infinity.
Note:
  • 24 pages, 1 figure, minor edits in v2
  • Scattering Amplitudes
  • Classical Theories of Gravity
  • Space-Time Symmetries
  • scattering: gravitation
  • gravitation: classical
  • symmetry: Kac-Moody
  • energy: flux
  • S-matrix
  • graviton
  • conservation law