Quasinormal modes of rotating black holes beyond general relativity in the WKB approximation

TL;DR

This paper extends the WKB approximation method to compute quasinormal modes of rotating black holes in theories beyond general relativity, demonstrating high accuracy relevant for gravitational wave observations.

Contribution

It develops higher-order WKB calculations for Kerr black holes in modified gravity theories and validates their accuracy against established methods.

Findings

WKB method achieves better accuracy than measurement errors for GW250114.

Extended WKB to higher order improves QNM spectrum calculations for rotating black holes.

WKB approximation remains effective beyond general relativity in complex gravity theories.

Abstract

Exploring gravitational theories beyond general relativity (GR) with black hole (BH) spectroscopy requires accurate and flexible methods for computing their quasinormal mode (QNM) spectrum. A popular method of choice is the higher-order Wentzel-Kramers-Brillouin (WKB) approximation, mostly applied to nonrotating BHs. While previous studies demonstrated that the higher-order WKB method can also be used for Kerr BHs in GR, there has been little work on rotating BHs in modified theories of gravity. In this work, we revive the idea by extending WKB calculations of the Kerr QNM spectrum to higher order and assessing its accuracy against continued-fraction tabulated data. We then apply the WKB approximation beyond GR, comparing it against both linearized and continued fraction calculations in the parametrized beyond-Teukolsky formalism and in higher-derivative gravity (HDG) theories. We find that the frequencies computed by the WKB method in theories beyond GR have better accuracy than the measurement errors for GW250114, the event with the highest ringdown signal-to-noise ratio observed to date.