Quasinormal behavior of the D-dimensional Schwarzshild black hole and higher order WKB approach

TL;DR

This paper analyzes the quasinormal modes of D-dimensional Schwarzschild black holes, deriving an asymptotic formula and extending the WKB method to sixth order for more accurate frequency calculations.

Contribution

It introduces a sixth-order WKB approach for computing quasinormal modes and derives a proportionality relation for the real parts of these modes in D-dimensional Schwarzschild black holes.

Findings

Real parts of QN modes scale with D and inverse horizon radius

Derived an asymptotic formula for large multipole number l and arbitrary D

Extended WKB method to sixth order for improved accuracy

Abstract

We study characteristic (quasinormal) modes of a $D$-dimensional Schwarzshild black hole. It proves out that the real parts of the complex quasinormal modes, representing the real oscillation frequencies, are proportional to the product of the number of dimensions and inverse horizon radius $\sim D r_{0}^{-1}$. The asymptotic formula for large multipole number $l$ and arbitrary $D$ is derived. In addition the WKB formula for computing QN modes, developed to the 3rd order beyond the eikonal approximation, is extended to the 6th order here. This gives us an accurate and economic way to compute quasinormal frequencies.