Abstract
This paper is motivated by the problem of the nonlinear stability of the Kerr solution for axially symmetric perturbations. We consider a model problem concerning the axially symmetric perturbations of a wave map Φ defined from a fixed Kerr solution K(M, a) , 0 ≤ a≤ M, with values in the two dimensional hyperbolic space H2. A particular such wave map is given by the complex Ernst potential associated to the axial Killing vector-field Z of K(M, a). We conjecture that this stationary solution is stable, under small axially symmetric perturbations, in the domain of outer communication (DOC) of K(M, a) , for all 0 ≤ a< M and we provide preliminary support for its validity, by deriving convincing stability estimates for the linearized system.
Original language | English (US) |
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Article number | 1 |
Journal | Annals of PDE |
Volume | 1 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1 2015 |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
- Geometry and Topology
- Mathematical Physics
- General Physics and Astronomy
Keywords
- Axially symmetric
- Kerr
- Morawetz
- Nonlinear
- Red shift
- Stability
- Trapping