Quasinormal modes of Schwarzschild black holes in four and higher dimensions

TL;DR

This paper investigates the asymptotic quasinormal modes of Schwarzschild black holes in four and five dimensions, confirming analytical predictions and extending corrections to higher dimensions with numerical validation.

Contribution

It provides numerical and analytical analysis of quasinormal modes in higher-dimensional Schwarzschild black holes, extending previous work and confirming the convergence behavior of the modes.

Findings

Numerical results support analytical predictions for leading terms.

First-order corrections are computed and match numerical data.

Convergence to asymptotic values is faster in five dimensions.

Abstract

We make a thorough investigation of the asymptotic quasinormal modes of the four and five-dimensional Schwarzschild black hole for scalar, electromagnetic and gravitational perturbations. Our numerical results give full support to all the analytical predictions by Motl and Neitzke, for the leading term. We also compute the first order corrections analytically, by extending to higher dimensions, previous work of Musiri and Siopsis, and find excellent agreement with the numerical results. For generic spacetime dimension number D the first-order corrections go as $\frac{1}{n^{(D-3)/(D-2)}}$. This means that there is a more rapid convergence to the asymptotic value for the five dimensional case than for the four dimensional case, as we also show numerically.