# Quasinormal modes of black holes. The improved semianalytic approach

## TL;DR

This paper improves the semianalytic method for calculating black hole quasinormal modes by using Padé approximants, achieving high accuracy for Schwarzschild and Reissner-Nordström black holes, and discusses potential generalizations.

## Contribution

The authors extend the Iyer-Will semianalytic technique by incorporating Padé approximants to enhance the accuracy of quasinormal frequency calculations.

## Key findings

- Padé approximants provide excellent agreement with numerical results
- The method is effective for Schwarzschild and Reissner-Nordström black holes
- Potential for generalization to other black hole classes

## Abstract

We have extended the semianalytic technique of Iyer and Will for computing the complex quasinormal frequencies of black holes, $\omega,$ by constructing the Pad\'e approximants of the (formal) series for $\omega^{2}$. It is shown that for the (so far best documented) quasinormal frequencies of the Schwarzschild and Reissner-Nordstr\"om black holes the Pad\'e transforms $P_{6}^{6}$ and $P_{7}^{6}$ are, within the domain of applicability, always in excellent agreement with the numerical results. We argue that the method may serve as the black box with the "potential" $Q(x)$ as an input and the accurate quasinormal modes as the output. The generalizations and modifications of the method are briefly discussed as well as the preliminary results for other classes of the black holes.