2016/02/08 by M. J. Taylor, Taylor, Martin, Martin Taylor · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Gamma-ray bursts and supernovae #Gas Dynamics and Kinetic Theory #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1602.02611
openalex publication_date 2016/02/08 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28
Minkowski space is shown to be globally stable as a solution to the\nEinstein--Vlasov system in the case when all particles have zero mass. The\nproof proceeds by showing that the matter must be supported in the "wave zone",\nand then proving a small data semi-global existence result for the\ncharacteristic initial value problem for the massless Einstein--Vlasov system\nin this region. This relies on weighted estimates for the solution which, for\nthe Vlasov part, are obtained by introducing the Sasaki metric on the mass\nshell and estimating Jacobi fields with respect to this metric by geometric\nquantities on the spacetime. The stability of Minkowski space result for the\nvacuum Einstein equations is then appealed to for the remaining regions.\n