Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8255892 | Journal of Geometry and Physics | 2018 | 47 Pages |
Abstract
We prove uniform decay estimates in the entire exterior of the Schwarzschild black hole for gauge invariant norms on the Yang-Mills fields valued in the Lie algebra associated to the Lie group SU(2). We assume that the initial data are spherically symmetric satisfying a certain Ansatz, and have small energy, which eliminates the stationary solutions which do not decay. In particular, there do not exist any Coulomb type solutions satisfying this Ansatz. We first prove a Morawetz type estimate for the Yang-Mills fields within this setting, using the Yang-Mills equations directly. We then adapt the proof constructed in previous work by the first author to show local energy decay and uniform decay of the Lâ norm of the middle components in the entire exterior of the Schwarzschild black hole, including the event horizon.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Sari Ghanem, Dietrich Häfner,