An approach to quasinormal modes of black hole based on reversed harmonic oscillator dynamics

TL;DR

This paper investigates the quasinormal modes of Schwarzschild black holes using reversed harmonic oscillator eigenstates, providing insights into scattering properties and mode frequencies through a novel quantum mechanical approach.

Contribution

It introduces a new method employing reversed harmonic oscillator eigenstates to analyze black hole quasinormal modes and scattering coefficients.

Findings

Calculated transmission and reflection coefficients for black hole scattering.

Derived quasinormal mode frequencies using the reversed harmonic oscillator framework.

Provided a new perspective on black hole perturbation analysis.

Abstract

The frequencies of quasinormal modes (QNM) for the Schwartzschild black hole are studied from the viewpoint of the particle scattering under an effective Regge-Wheeler type of potential consisting of a parabolic type one in an intermediate region and flat potentials on both sides. In particular, we use the eigenstates for a reversed harmonic oscillator as the complete bases in this intermediate region. Under this setting, the transmission and reflection coefficients are studied in addition to the frequencies of QNMs.