Quasinormal modes in higher derivative gravity: testing the black hole parametrization and sensitivity of overtones

TL;DR

This paper investigates how higher overtones of black hole quasinormal modes in Einstein-Weyl gravity are highly sensitive to small corrections, impacting black hole ringdown modeling and proposing an improved metric parametrization method.

Contribution

It demonstrates the sensitivity of overtones to Weyl corrections and introduces an extended parametrization approach to accurately approximate black hole metrics.

Findings

Overtones are highly sensitive to Weyl term corrections.

Third-order metric approximation can cause nonmonotonic frequency behavior.

Higher-order parametrization stabilizes frequency predictions.

Abstract

The fundamental quasinormal modes of black holes in higher-derivative gravity given by the Einstein-Weyl action are known to be moderately corrected by the Weyl term. Here we will show that the first several overtones are highly sensitive to even a relatively small Weyl correction, which might be important when representing the earlier stage of the black hole ringdown. In addition, we have solved the problem related to the analytical parametrized approximation of the numerical black hole solution in the Einstein-Weyl theory: In some range of parameters the approximation for the metric developed up to the third order leads to the unusual highly nonmonotonic behavior of the frequencies. We have shown that this problem can be solved via the extension of the parametrization of the metric to higher orders until reaching the regime when the frequencies do not change with further increasing of the order.