Quasi-normal modes for Dirac fields in the Kerr–Newman–de Sitter black holes

Abstract

We provide the full asymptotic description of the quasi-normal modes (resonances) in any strip of fixed width for Dirac fields in slowly rotating Kerr-Newman-de Sitter black holes. The resonances split in a way similar to the Zeeman effect. The method is based on the extension to Dirac operators of techniques applied by Dyatlov in [17], [18] to the (uncharged) Kerr-de Sitter black holes. We show that the mass of the Dirac field does not have effect on the two leading terms in the expansions of resonances.

Quasi-normal modes for de Sitter–Reissner–Nordström black holes

“…As the last problem is well studied, we can easily transmit many already existing results to the Dirac case, and apply the Birkhoff normal form construction. Note also that the formulas obtained in this paper for the massless uncharged case indicate what one should expect to get in the general case as it is believed that, due to intense gravitation near the event and cosmological horizons of the black hole, even if the Dirac fields are massive, they propagate asymptotically as in the massless case (see [27], [40]).…”

“…Note also the paper [18], where the authors extended their inverse scattering results from [17] to the scattering for massless Dirac fields by the (rotating) Kerr-Newman-de Sitter black holes. It appears that the techniques of Dyatlov used in [20], [21] can be adapted to the framework of Dirac operators for the Kerr-Newman-de Sitter black holes (see [40]).…”

Resonance expansions of massless Dirac fields propagating in the exterior of a de Sitter–Reissner–Nordström black hole

“…The formulas obtained in this paper for the massless uncharged case indicate what one should expect to get in the general case as it is believed that, due to intense gravitation near the event and cosmological horizons of the black hole, even if the Dirac fields are massive, they propagate asymptotically as in the massless case (see [21], [30]).…”

“…As the last problem is well studied, we can easily transmit many already existing results to the Dirac case, and apply the Birkhoff normal form construction. This paper is the second one in our project on quasi-normal modes for Dirac fields in black holes geometry and many properties and methods from this model can be generalized to more complicated situations as the cases of massive charged Dirac fields and rotating (Kerr-Newman) black holes (see [30] and forthcoming papers).…”

Explicit formula and meromorphic extension of the resolvent for the massive Dirac operator in the Schwarzschild-anti-de Sitter spacetime

“…This was then extended to space-times close to the Kerr-de Sitter family by A. Vasy [32]. These techniques were also adapted by A. Iantchenko to the study of resonances for Dirac fields in the Kerr-Newman-de Sitter spacetime [23]. This work follows some other works by the same author concerning resonances for the Dirac fields in the de Sitter-Reissner-Nordström black holes where an expansion in terms of resonances was obtained [24].…”