2024/02/27 by Arthur Touati, Touati, Arthur · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · pdf · doi:10.48550/arxiv.2402.17530
openalex publication_date 2024/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a regular solution g0 of the Einstein-null dusts system without restriction on the number of dusts, we construct families of solutions (gλ)λ∈(0,1] of the Einstein vacuum equations such that gλ-g0 and ∂(gλ-g0) converges respectively strongly and weakly to 0 when λ→0. Our construction, based on a multiphase geometric optics ansatz, thus extends the validity of the reverse Burnett conjecture without symmetry to a large class of massless kinetic spacetimes. In order to deal with the finite but arbitrary number of direction of oscillations we work in a generalised wave gauge and control precisely the self-interaction of each wave but also the interaction of waves propagating in different null directions, relying crucially on the non-linear structure of the Einstein vacuum equations. We also provide the construction of oscillating initial data solving the vacuum constraint equations and which are consistent with the spacetime ansatz.