  This paper studies diagonal spacetime metrics. It is shown that the
overdetermined Einstein vacuum equations are compatible if one Killing vector
exists. The stability of plane gravitational waves of the Robinson type is
studied. This stability problem bares a fantastic mathematical resemblance to
the stability of the Schwarzschild black hole studied by Regge and Wheeler.
Just like for the Schwarzschild black hole, the Robinson gravitational waves
are proven to be stable with respect to small perturbations. We conjecture that
a bigger class of vacuum solutions are stable, among which are all
gravitational solitons. Moreover, the stability analysis reveals a surprising
fact: a wave barrier will be transparent to the Robinson waves, which therefore
passes through the barrier freely. This is a hint of integrability of the 1+2
vacuum Einstein equations for diagonal metrics.
