High overtones of Schwarzschild-de-Sitter quasinormal spectrum

TL;DR

This paper investigates the high overtone quasinormal modes of Schwarzschild-de Sitter black holes, revealing oscillatory behaviors in the real parts of frequencies and confirming numerical results with WKB methods.

Contribution

It provides new insights into the asymptotic behavior of gravitational and electromagnetic quasinormal modes at high overtones for Schwarzschild-de Sitter black holes.

Findings

Electromagnetic modes' real parts approach zero at high overtones.

Gravitational modes exhibit oscillating real parts as overtone number increases.

Numerical results agree well with 6th order WKB calculations.

Abstract

We find the high overtones of gravitational and electromagnetic quasinormal spectrum of the Schwarzschild-de Sitter black hole. The calculations show that the real parts of the electromagnetic modes asymptotically approach zero. The gravitational modes show more peculiar behavior at large $n$: the real part oscillates as a function of imaginary even for very high overtones and these oscillations settles to some "profile" which just repeats itself with further increasing of the overtone number $n$. This lets us judge that $Re \omega$ is not a constant as $n \to \infty$ but rather some oscillating function. The spacing for imaginary part $ Im \omega_{n+1}-Im \omega_{n}$ for both gravitational and electromagnetic perturbations at high $n$ oscillates as a function of $n$ around the value $k_{e}$, where $k_{e}$ is the surface gravity. In addition we find the lower QN modes for which the values obtained with numerical methods are in a very good agreement with those obtained through the 6th order WKB technique.