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Local Propagation of Impulsive Gravitational Waves

Author(s): Luk, Jonathan; Rodnianski, Igor

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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. (C) 2015 Wiley Periodicals, Inc.
Publication Date: Apr-2015
Electronic Publication Date: 21-Jul-2014
Citation: Luk, Jonathan, Rodnianski, Igor. (2015). E Local Propagation of Impulsive Gravitational Waves. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 68 (511 - 624. doi:10.1002/cpa.21531
DOI: doi:10.1002/cpa.21531
ISSN: 0010-3640
EISSN: 1097-0312
Pages: 511 - 624
Type of Material: Journal Article
Version: Author's manuscript

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