Identifying modified theories of gravity using binary black-hole ringdowns

TL;DR

Black-hole spectroscopy can effectively detect small deviations from Kerr black hole spectra in general relativity, with next-generation detectors capable of identifying 1% frequency shifts at feasible signal-to-noise ratios.

Contribution

This study systematically evaluates the ability of black-hole spectroscopy to identify various theoretically motivated and phenomenological deviations from Kerr spectra.

Findings

A 1% shift in fundamental mode frequencies can be detected with signal-to-noise ratios between 150 and 500.

Next-generation detectors can achieve the required sensitivity for such detections.

Black-hole spectroscopy offers a promising method to test deviations from general relativity.

Abstract

Black-hole spectroscopy, that is, measuring the characteristic frequencies and damping times of different modes in a black-hole ringdown, is a powerful probe for testing deviations from the general theory of relativity (GR). In this work, we present a comprehensive study on its ability to identify deviations from the spectrum of a Kerr black hole in GR. Specifically, we investigate the performance of black hole spectroscopy on a diverse set of theoretically motivated as well as phenomenologically modified spectra. We find that while the signal-to-noise ratio $\rho_{\rm RD}$ in the ringdown required to identify a modification to the GR Kerr black hole spectrum depends on the details of the modifications, a modification that introduces $\sim 1 \%$ shift in the fundamental mode frequencies can typically be distinguished with $\rho_{\rm RD} \in [150,500]$. This range of $\rho_{\rm RD}$ is feasible with the next-generation detectors, showing a promising science case for black hole spectroscopy.