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Ambient Metrics for n-Dimensional pp-Waves

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Abstract

We provide an explicit formula for the Fefferman-Graham ambient metric of an n-dimensional conformal pp-wave in those cases where it exists. In even dimensions we calculate the obstruction explicitly. Furthermore, we describe all 4-dimensional pp-waves that are Bach-flat, and give a large class of Bach-flat examples which are conformally Cotton-flat, but not conformally Einstein. Finally, as an application, we use the obtained ambient metric to show that even-dimensional pp-waves have vanishing critical Q-curvature.

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Authors and Affiliations

  1. School of Mathematical Sciences, The University of Adelaide, Adelaide, SA, 5005, Australia

    Thomas Leistner

  2. Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, ul. Hoża 69, 00-681, Warszawa, Poland

    Pawel Nurowski

  3. Instytut Matematyczny PAN, ul. Sniadeckich 8, 00-956, Warszawa, Poland

    Pawel Nurowski

Authors
  1. Thomas Leistner
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  2. Pawel Nurowski
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Correspondence to Thomas Leistner.

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Communicated by P.T. Chruściel

This work was supported in part by the Polish Ministerstwo Nauki i Informatyzacji grant nr: 1 P03B 07529 and by the Sonderforschungsbereich 676 of the German Research Foundation.

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Leistner, T., Nurowski, P. Ambient Metrics for n-Dimensional pp-Waves. Commun. Math. Phys. 296, 881–898 (2010). https://doi.org/10.1007/s00220-010-0995-x

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