Stable and decaying bound states on the naked Reissner-Nordstr\"om background

TL;DR

This paper investigates quantum bound states of a scalar particle in a naked Reissner-Nordström spacetime, revealing both stable and decaying states, with metastable states being longer-lived than black hole quasinormal modes.

Contribution

It provides the first analysis of bound states on a naked RN background, including their spectra and comparison with black hole quasinormal modes.

Findings

Existence of both stable and metastable bound states.

Metastable states are longer-lived than black hole quasinormal modes.

Energy spectra are calculated using the WKB approximation.

Abstract

We present a quantum mechanical study of the bound states of a neutral scalar particle on the curved background described by the Reissner-Nordstr\"om (RN) spacetime that corresponds to a naked singularity. We show that there occurs both the metastable, \textit{i.e.} decaying bound states and the stable ones. The corresponding energy spectra are calculated in the leading WKB approximation and the comparison with the RN black hole quasinormal mode spectrum is made. The metastable bound states on the naked singularity background turn out to be more long-living than the quasinormal modes for the black hole with the same mass.