Quasi-normal modes ratios as agnostic test of general relativity

TL;DR

This paper introduces a new, model-agnostic method for testing general relativity using black hole ringdown mode ratios, which are largely independent of black hole mass and sensitive to deviations predicted by alternative theories.

Contribution

The paper proposes a novel test based on mode frequency and damping time ratios, providing a semi-analytical explanation and demonstrating its effectiveness in distinguishing GR from alternative theories.

Findings

Ratios vary little with black hole spin

Ratios depend mainly on mode angular momentum and overtone number

Ratios in alternative theories differ significantly from GR predictions

Abstract

In this letter, we provide a novel test of general relativity based on ringdown analysis. The test is performed on agnostic models, where the postmerger signal is fitted with a superposition of damped sinusoids. If at least two modes are detected, one has to compute the ratio of the frequencies and of the damping times and compare them against the predictions of general relativity. By considering ratios, the dependency on the black hole's mass is scaled away. Most notably, we find that the ratios vary very little with the spin, the real part depends mostly on the angular momentum of the mode $\ell$ and the imaginary part depends mostly on the overtone number $n$: different combinations create specific mode islands. We provide a qualitative explanation of these islands through a semi-analytical argument. We discuss the application of the method to future detectors. Finally, we show that ratios in alternative theories of gravity or between different field content drastically differ from those of general relativity.