For subextremal Kerr spacetimes, the paper constructs a positive-definite, conserved Hamiltonian energy for axially symmetric linear perturbations, indicating a form of linear stability within this symmetry class.
On the global stability of the wave-map equation in Kerr spaces with small angular momentum
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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 $\Phi$ defined from a fixed Kerr solution $\KK(M,a)$, $0\le a < M $, with values in the two dimensional hyperbolic space $\HHH^2$. A particular such wave map is given by the complex Ernst potential associated to the axial Killing vectorfield $\Z$ of $\KK(M,a)$. We conjecture that this stationary solution is stable, under small axially symmetric perturbations, in the domain of outer communication (DOC) of $\KK(M,a)$, for all $0\le a<M$ and we provide preliminary support for its validity, by deriving convincing stability estimates for the linearized system.
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gr-qc 1years
2025 1verdicts
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On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
For subextremal Kerr spacetimes, the paper constructs a positive-definite, conserved Hamiltonian energy for axially symmetric linear perturbations, indicating a form of linear stability within this symmetry class.