Perturbative calculation of quasi-normal modes of arbitrary spin in Schwarzschild spacetime

TL;DR

This paper analytically computes the asymptotic quasi-normal modes of arbitrary spin perturbations in Schwarzschild spacetime, including first-order corrections, and confirms the results with numerical data for fermions.

Contribution

It provides explicit analytical expressions for quasi-normal modes of arbitrary spin in Schwarzschild spacetime, extending previous methods and including first-order corrections.

Findings

Expressions match those from Regge-Wheeler equation for integer spins.

Zeroth-order results agree with WKB analysis.

Results for Dirac fermions align well with numerical data.

Abstract

We calculate analytically the asymptotic form of quasi-normal modes of perturbations of arbitrary spin of a Schwarzschild black hole including first-order corrections. We use the Teukolsky equation which applies to both bosonic and fermionic modes. Remarkably, we arrive at explicit expressions which coincide with those derived using the Regge-Wheeler equation for integer spin. Our zeroth-order expressions agree with the results of WKB analysis. In the case of Dirac fermions, our results are in good agreement with numerical data.