2011/11/30 by Gustavo Dotti, Reinaldo J. Gleiser, Reinaldo J Gleiser +2 · 1 citation
Physics and Astronomy · #Astrophysical Phenomena and Observations #Axial symmetry #Black Holes and Theoretical Physics #Boundary value problem #Field (mathematics) #Killing vector field #Naked singularity #Pulsars and Gravitational Waves Research #Ring singularity #Rotating black hole #Singularity #Spacetime #gr-qc
paper · pdf · doi:10.1088/0264-9381/29/9/095017
published as Class.Quant.Grav. 29 (2012) 095017
openalex publication_date 2012/04/16 · arxiv created 2012/08/09 · arxiv updated 2012/08/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show that both the interior region 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 timelike, and the Teukolsky equation, restricted to axially symmetric fields, changes its character from hyperbolic to elliptic.