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Hertz Potentials and Asymptotic Properties of Massless Fields

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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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Author notes

  1. Thomas Bäckdahl

    Present address: The School of Mathematics, The University of Edinburgh, JCMB 6228, The King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK

  2. Jérémie Joudioux

    Present address: Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1050, Wien, Austria

Authors and Affiliations

  1. Albert Einstein Institute, Am Mühlenberg 1, 14476, Potsdam, Germany

    Lars Andersson, Thomas Bäckdahl & Jérémie Joudioux

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  1. Lars Andersson
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  2. Thomas Bäckdahl
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  3. Jérémie Joudioux
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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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