The conformal Einstein field equations and the local extension of future null infinity

We make use of an improved existence result for the characteristic initial value problem for the conformal Einstein equations to show that given initial data on two null hypersurfaces N⋆ and N⋆′ such that the conformal factor (but not its gradient) vanishes on a section of N⋆, one recovers a portion...

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Bibliographic Details
Published in:Journal of mathematical physics 2021-10, Vol.62 (10)
Main Authors: Zhao, Peng, Hilditch, David, Valiente Kroon, Juan A.
Format: Article
Language:English
Subjects:
Boundary value problems
Einstein equations
Hyperspaces
Infinity
Mathematical analysis
Minkowski space
Physics
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Summary:We make use of an improved existence result for the characteristic initial value problem for the conformal Einstein equations to show that given initial data on two null hypersurfaces N⋆ and N⋆′ such that the conformal factor (but not its gradient) vanishes on a section of N⋆, one recovers a portion of null infinity. This result combined with the theory of the hyperboloidal initial value problem for the conformal Einstein field equations allows us to show the semi-global stability of the Minkowski spacetime from characteristic initial data.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0056969