2021/07/02 by A Guerra, Guerra, André, Rita Teixeira da Costa +1
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · pdf · doi:10.48550/arxiv.2107.00942
openalex publication_date 2021/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein--massless Vlasov system. In a recent breakthrough, Huneau--Luk (arXiv:1907.10743) gave a proof of the conjecture in U(1)-symmetry and elliptic gauge. They also require control on up to fourth order derivatives of the metric components. In this paper, we give a streamlined proof of a stronger result and, in the spirit of Burnett's original conjecture, we remove the need for control on higher derivatives. Our methods also apply to general wave map equations.