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

TL;DR

This paper investigates the quasinormal modes of scalar fields in a naked Reissner-Nordström spacetime, revealing qualitative differences from black hole cases and providing evidence that highly damped modes are absent, supporting conjectures about horizon-related properties.

Contribution

It analyzes the existence and characteristics of quasinormal modes in naked Reissner-Nordström spacetimes, highlighting the absence of highly damped modes and their relation to horizon properties.

Findings

Different behavior of quasinormal modes depending on charge-to-mass ratio

Absence of highly damped quasinormal modes in naked singularity case

Conditions for well-posedness of scalar field scattering problem

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-Nordstr\"om 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-Nordstr\"om singularity, corroborating recent conjectures relating them to classical and quantum properties of horizons.