Ambient metrics for $n$-dimensional $pp$-waves
Differential Geometry
2015-05-13 v3 High Energy Physics - Theory
Abstract
We provide an explicit formula for the Fefferman-Graham-ambient metric of an -dimensional conformal -wave in those cases where it exists. In even dimensions we calculate the obstruction explicitly. Furthermore, we describe all 4-dimensional -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 -waves have vanishing critical -curvature.
Cite
@article{arxiv.0810.2903,
title = {Ambient metrics for $n$-dimensional $pp$-waves},
author = {Thomas Leistner and Pawel Nurowski},
journal= {arXiv preprint arXiv:0810.2903},
year = {2015}
}
Comments
17 pages, in v2 footnote and references added and typos corrected, in v3 remark in the Introduction about Brinkmann's results corrected and footnote added