2016/10/26 by Pei-Ken Hung, Hung, Pei-Ken, Jordan Keller +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.AP #math.DG
paper · pdf · doi:10.48550/arxiv.1610.08547
38 pages
arxiv created 2016/10/28 · arxiv updated 2017/02/10
In this paper, we address the issue of linear stability of Schwarzschild space- time subject to certain axisymmetric perturbations. In particular, we prove that associ- ated solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, decay to a linearized Kerr metric. Our method employs a complex line bundle interpretation applied to a connection-level object, allow- ing for direct analysis of this connection-level object by the linearized Einstein equations, in contrast with the recent breakthrough of Dafermos-Holzegel-Rodnianski.