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.

v3: 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

References in corpus (5)

• The physical interpretation of the spectrum of black hole quasinormal modes
• Quasi-normal frequencies: Key analytic results
• Instability of charged and rotating naked singularities
• Quantum Singularities in Static Spacetimes
• Quasi-normal modes, area spectra and multi-horizon spacetimes

Cited by in corpus (5)

• Transition from Regular Black Holes to Wormholes in Covariant Effective Quantum Gravity: Scattering, Quasinormal Modes, and Hawking Radiation
• Black holes in massive gravity: Quasi-normal modes of scalar perturbations
• Quasinormal modes and self-adjoint extensions of the Schroedinger operator
• No asymptotically highly damped quasi-normal modes without horizons?
• Null geodesics in five-dimensional Reissner-Nordström anti-de Sitter black hole