Double Null Data and the Characteristic Problem in General Relativity

Abstract

General hypersurfaces of any causal character can be studied abstractly using the hypersurface data formalism. In the null case, we write down all tangential components of the ambient Ricci tensor in terms of the abstract data. Using this formalism, we formulate and solve in a completely abstract way the characteristic Cauchy problem of the Einstein vacuum field equations. The initial data is detached from any spacetime notion, and it is fully diffeomorphism and gauge covariant. The results of this paper put the characteristic problem on a similar footing as the standard Cauchy problem in General Relativity.

arXiv commentThe presentation of the proof of Theorem 7.15 has been improved. Several typos has been amended. Some long computations has been moved to appendices

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• Transverse expansion of the metric at null hypersurfaces I. Uniqueness and application to Killing horizons
• Transverse expansion of the metric at null hypersurfaces II. Existence results and application to Killing horizons
• Unique Carrollian manifolds emerging from Einstein spacetimes
• Gravitational null rays: Covariant Quantization and the Dressing Time
• Killing and homothetic initial data for general hypersurfaces