2020/06/23 by David Hilditch, Hilditch, David, Juan A. Valiente Kroon +3 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2006.13757
openalex publication_date 2020/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We adapt Luk's analysis of the characteristic initial value problem in General Relativity to the asymptotic characteristic problem for the conformal Einstein field equations to demonstrate the local existence of solutions in a neighbourhood of the set on which the data are given. In particular, we obtain existence of solutions along a narrow rectangle along null infinity which, in turn, corresponds to an infinite domain in the asymptotic region of the physical spacetime. This result generalises work by Kánnár on the local existence of solutions to the characteristic initial value problem by means of Rendall's reduction strategy. In analysing the conformal Einstein equations we make use of the Newman-Penrose formalism and a gauge due to J. Stewart.