2023/08/24 by Yuchen Mao, Mao, Yuchen, Sung‐Jin Oh +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2308.13031
openalex publication_date 2023/08/24 · openalex created_date 2023/08/29 · openalex updated_date 2026/07/28
We give new proofs of general relativistic initial data gluing results on unit-scale annuli based on explicit solution operators for the linearized constraint equation around the flat case with prescribed support properties. These results retrieve and optimize - in terms of positivity, regularity, size and/or spatial decay requirements - a number of known theorems concerning asymptotically flat initial data, including Kerr exterior gluing by Corvino-Schoen and Chruściel-Delay, interior gluing (or "fill-in") by Bieri-Chruściel, and obstruction-free gluing by Czimek-Rodnianski. In particular, our proof of the strengthened obstruction-free gluing theorem relies on purely spacelike techniques, rather than null gluing as in the original approach.