Revisiting the characteristic initial value problem for the vacuum Einstein field equations

Using the Newman–Penrose formalism we study the characteristic initial value problem in vacuum General Relativity. We work in a gauge suggested by Stewart, and following the strategy taken in the work of Luk, demonstrate local existence of solutions in a neighbourhood of the set on which data are gi...

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Bibliographic Details
Published inGeneral relativity and gravitation Vol. 52; no. 10
Main Authors Hilditch, David, Valiente Kroon, Juan A., Zhao, Peng
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2020
Springer Nature B.V
Subjects
Astronomy
Astrophysics and Cosmology
Boundary value problems
Classical and Quantum Gravitation
Differential Geometry
Einstein equations
Gravity
Hyperspaces
Mathematical analysis
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity
Relativity Theory
Research Article
Theoretical
Characteristic problem
Newman-Penrose formalism
Initial value problem
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Summary:Using the Newman–Penrose formalism we study the characteristic initial value problem in vacuum General Relativity. We work in a gauge suggested by Stewart, and following the strategy taken in the work of Luk, demonstrate local existence of solutions in a neighbourhood of the set on which data are given. These data are given on intersecting null hypersurfaces. Existence near their intersection is achieved by combining the observation that the field equations are symmetric hyperbolic in this gauge with the results of Rendall. To obtain existence all the way along the null-hypersurfaces themselves, a bootstrap argument involving the Newman–Penrose variables is performed.
ISSN:0001-7701
1572-9532
DOI:10.1007/s10714-020-02747-2