Linear stability of Schwarzschild spacetime subject to axial perturbations

Pei-Ken Hung; Jordan Keller

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arXiv · 1610.08547

Linear stability of Schwarzschild spacetime subject to axial perturbations

Pei-Ken Hung·Jordan Keller

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Abstract

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.

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Pei-Ken Hung, Jordan Keller. 2016-10-26. Linear stability of Schwarzschild spacetime subject to axial perturbations. https://arxiv.org/abs/1610.08547

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