The failure of the Ehlers--Kundt conjecture in the impulsive case

Moriz L. Frauenberger, James D. E. Grant, Roland Steinbauer

In 1962, Ehlers and Kundt conjectured that plane waves are the only class of complete Ricci-flat~\emph{pp}-waves, i.e.\ metrics on ${\mathbb{R}}^4$ of the form \[ ds^2=2du\,dv+dx^2+…