Quasinormal modes for the scattering on a naked Reissner-Nordstrom singularity

Abstract

What should be the quasinormal modes associated with a spacetime that contains a naked singularity instead of a black hole? In the present work we address this problem by studying the scattering of scalar fields on a curved background described by a Reissner-Nordström spacetime with $|q|>m$. We show that there is a qualitative difference between cases with $1<q^2/m^2\lesssim 9/8$ and cases with $q^2/m^2\gtrsim 9/8$. We discuss the necessary conditions for the well-posedness of the problem, and present results for the low damped modes in the low $l$ and large $l$ limit. We also consider the asymptotically highly damped quasinormal modes. We present strong evidence that such modes are absent in the case of a naked Reissner-Nordström singularity, corroborating recent conjectures relating them to classical and quantum properties of horizons.

arXiv commentv3: final version to appear in Physical Review D, 17 pages, 10 figures, v3: only minor cosmetic changes (few typos corrected) with respect to v2, v1: the same physics, but missing one section

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• Null geodesics in five-dimensional Reissner-Nordström anti-de Sitter black hole
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• Stable and decaying bound states on the naked Reissner-Nordström background