Transparency of strong gravitational waves

Y. Hadad, V. Zakharov

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)37-48
Number of pages12
JournalJournal of Geometry and Physics
Publication statusPublished - Jun 2014
Externally publishedYes


  • Einstein's field equations
  • General relativity
  • Gravitational solitons
  • Gravitational waves
  • Integrable systems
  • Stability


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