Unstable fields in Kerr spacetimes

Abstract

We show that both the interior region $r<M-\sqrt{M^2-a^2}$ of a Kerr black hole and the $a^2>M^2$ Kerr naked singularity admit unstable solutions of the Teukolsky equation for any value of the spin weight. For every harmonic number there is at least one axially symmetric mode that grows exponentially in time and decays properly in the radial directions. These can be used as Debye potentials to generate solutions for the scalar, Weyl spinor, Maxwell and linearized gravity field equations on these backgrounds, satisfying appropriate spatial boundary conditions and growing exponentially in time, as shown in detail for the Maxwell case. It is suggested that the existence of the unstable modes is related to the so called "time machine" region, where the axial Killing vector field is time-like, and the Teukolsky equation, restricted to axially symmetric fields, changes its character from hyperbolic to elliptic.

References in corpus (6)

• Appearance of Keplerian discs orbiting Kerr superspinars
• Gravitational instabilities of superspinars
• Instability of the negative mass Schwarzschild naked singularity
• Instability of charged and rotating naked singularities
• Gravitational instabilities in Kerr space-times
• Instabilities of naked singularities and black hole interiors in General Relativity

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• Distinguishing Brans-Dicke-Kerr type naked singularities and black holes with their thin disk electromagnetic radiation properties
• Dynamics of current-carrying string loops in the Kerr naked-singularity and black-hole spacetimes
• Numerical relativity in higher dimensions
• Magnetised accretion discs in Kerr spacetimes
• Magnetised Accretion Discs in Kerr Spacetimes II: Hot Spots
• Linear Stability of Black Holes and Naked Singularities
• Effect of magnetic fields on equatorial circular orbits in Kerr spacetimes
• Scalar Resonances in Axially Symmetric Spacetimes