Double Null Data and the Characteristic Problem in General Relativity

Autor:	Mars, Marc, Sánchez-Pérez, Gabriel
Rok vydání:	2022
Předmět:	General Relativity and Quantum Cosmology Mathematics - Analysis of PDEs Mathematics - Differential Geometry
Zdroj:	Journal of Physics A: Mathematical and Theoretical, 2023
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8121/acb098
Popis:	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. Comment: The presentation of the proof of Theorem 7.15 has been improved. Several typos has been amended. Some long computations has been moved to appendices
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.15267 Zobrazit plný text záznamu View this record from Arxiv