Local propagation of impulsive gravitationalwaves

Jonathan Luk, Igor Rodnianski

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

In this paper, we initiate the rigorous mathematical study of the problem of impulsive gravitational spacetime waves. We construct such spacetimes as solutions to the characteristic initial value problem of the Einstein vacuum equations with a data curvature delta singularity. We show that in the resulting spacetime, the delta singularity propagates along a characteristic hypersurface, while away from that hypersurface the spacetime remains smooth. Unlike the known explicit examples of impulsive gravitational spacetimes, this work in particular provides the first construction of an impulsive gravitational wave of compact extent and does not require any symmetry assumptions. The arguments in the present paper also extend to the problem of existence and uniqueness of solutions to a larger class of nonregular characteristic data.

Original languageEnglish (US)
Pages (from-to)511-624
Number of pages114
JournalCommunications on Pure and Applied Mathematics
Volume68
Issue number4
DOIs
StatePublished - Apr 1 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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