Spin-1 Quasi-normal Frequencies in Schwarzschild space-time for Large Overtone Number

TL;DR

This paper analytically derives the high-overtone number asymptotic behavior of spin-1 quasinormal mode frequencies in Schwarzschild black holes, providing explicit formulas up to order n^{-5/2}.

Contribution

It introduces a formal expansion method to compute quasinormal frequencies to arbitrary order for large overtone numbers.

Findings

Explicit asymptotic formulas up to order n^{-5/2}

Formal expansion method for arbitrary order frequencies

Enhanced understanding of black hole perturbation spectra

Abstract

We analytically investigate the spin-1 quasinormal mode frequencies of Schwarzschild black hole space-time. We formally determine these frequencies to arbitrary order as an expansion for large imaginary part (i.e., large-n, where n is the overtone number). As an example of the practicality of this formal procedure, we explicitly calculate the asymptotic behaviour of the frequencies up to order $n^{-5/2}$.