Communications in Mathematical Physics

, Volume 296, Issue 3, pp 881–898 | Cite as

Ambient Metrics for n-Dimensional pp-Waves

Article

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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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.School of Mathematical SciencesThe University of AdelaideAdelaideAustralia
  2. 2.Instytut Fizyki TeoretycznejUniwersytet WarszawskiWarszawaPoland
  3. 3.Instytut Matematyczny PANWarszawaPoland

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