A semi-analytic treatment of quasinormal excitation factors in the eikonal regime

TL;DR

This paper introduces an improved semi-analytic method for calculating quasinormal excitation factors of Schwarzschild black holes in the eikonal regime, enhancing accuracy and aiding gravitational wave analysis.

Contribution

It extends existing techniques with higher-order corrections, providing more precise quasinormal mode excitation factors for black hole ringdown modeling.

Findings

Reduced relative error in quasinormal mode calculations

Excellent agreement with established methods

Enhanced capability to model gravitational wave signals

Abstract

In this paper, we present an enhanced semi-analytic method for calculating quasinormal excitation factors in the eikonal regime, specifically for Schwarzschild black holes. To achieve improved accuracy in our quasinormal mode computations, we extend the Dolan and Ottewill inverse multipolar expansion technique and incorporate higher-order corrections from the WKB method of Iyer and Will. Our approach is carried out to a higher order than previous methods, thereby reducing the relative error, particularly for lower multipolar numbers. We validate our results by comparing them with those obtained using the Mano, Suzuki, and Takasugi method, demonstrating excellent agreement. A key advantage of our method is its ability to extract quasinormal excitation factors, which are crucial for accurately modeling gravitational wave signals from binary black hole mergers. This advancement provides a useful tool for future gravitational wave studies, enabling better quantification of quasinormal mode excitations and more precise identification of individual modes during black hole ringdowns.