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Hertz Potentials and Asymptotic Properties of Massless Fields

Abstract

In this paper we analyze Hertz potentials for free massless spin-s fields on the Minkowski spacetime, with data in weighted Sobolev spaces. We prove existence and pointwise estimates for the Hertz potentials using a weighted estimate for the wave equation. This is then applied to give weighted estimates for the solutions of the spin-s field equations, for arbitrary half-integer s. In particular, the peeling properties of the free massless spin-s fields are analyzed for initial data in weighted Sobolev spaces with arbitrary, non-integer weights.

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Correspondence to Lars Andersson.

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Communicated by P. T. Chruściel

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Andersson, L., Bäckdahl, T. & Joudioux, J. Hertz Potentials and Asymptotic Properties of Massless Fields. Commun. Math. Phys. 331, 755–803 (2014). https://doi.org/10.1007/s00220-014-2078-x

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  • DOI: https://doi.org/10.1007/s00220-014-2078-x

Keywords

  • Initial Data
  • Wave Equation
  • Cauchy Problem
  • High Spin
  • Minkowski Space