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

Abstract

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.

arXiv comment58 pages, 4 figures

References in corpus (3)

• Global existence for the Einstein vacuum equations in wave coordinates
• The many ways of the characteristic Cauchy problem
• The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions

Cited by in corpus (7)

• Classical double copy at null infinity
• Gauge structure of the Einstein field equations in Bondi-like coordinates
• Double Null Data and the Characteristic Problem in General Relativity
• Covariant definition of Double Null Data and geometric uniqueness of the characteristic initial value problem
• Numerical convergence of model Cauchy-characteristic extraction and matching
• A symmetric hyperbolic formulation of the vacuum Einstein equations in affine-null coordinates
• The conformal Einstein field equations and the local extension of future null infinity