Perturbative Calculation of Quasinormal Modes of $d$--Dimensional Black Holes

TL;DR

This paper analytically calculates quasinormal modes of various $d$-dimensional black holes, including first-order corrections, revealing differences between charged and uncharged cases and supporting the view that certain numerical coincidences are accidental.

Contribution

It extends analytical methods to include first-order corrections for quasinormal modes across different black hole types, highlighting differences based on charge and dimensions.

Findings

First-order corrections differ for charged and uncharged black holes.

The method is not applicable to black holes with small charge.

The $ abla 3$ in $d=4$ Schwarzschild is likely a numerical coincidence.

Abstract

We study analytically quasinormal modes in a wide variety of black hole spacetimes, including $d$--dimensional asymptotically flat spacetimes and non-asymptotically flat spacetimes (particular attention has been paid to the four dimensional case). We extend the analytical calculation to include first-order corrections to analytical expressions for quasinormal mode frequencies by making use of a monodromy technique. All possible type perturbations are included in this paper. The calculation performed in this paper show that systematic expansions for uncharged black holes include different corrections with the ones for charged black holes. This difference makes them have a different $n$--dependence relation in the first-order correction formulae. The method applied above in calculating the first-order corrections of quasinormal mode frequencies seems to be unavailable for black holes with small charge. This result supports the Neitzke's prediction. On what concerns quantum gravity we confirm the view that the $\ln3$ in $d=4$ Schwarzschild seems to be nothing but some numerical coincidences.