Theory-agnostic Reconstruction of Potential and Couplings from Quasi-Normal Modes

TL;DR

This paper introduces a theory-agnostic method to reconstruct black hole perturbation potentials and couplings from quasi-normal mode observations, enabling tests of gravity theories without assuming a specific model.

Contribution

It develops a parametrized, theory-agnostic framework linking quasi-normal modes to perturbation equations, allowing potential and coupling reconstructions from observational data.

Findings

Percent-level measurements can constrain the effective potential and couplings.

The method successfully reconstructs potentials from simulated data in extended gravity theories.

It provides a model-independent way to test gravity using black hole ringdown signals.

Abstract

In this work, we use a parametrized theory-agnostic approach that connects the observation of black hole quasi-normal modes with the underlying perturbation equations, with the goal of reconstructing the potential and the coupling functions appearing in the latter. The fundamental quasi-normal mode frequency and its first two overtones are modeled through a second order expansion in the deviations from general relativity, which are assumed to be small but otherwise generic. By using a principal component analysis, we demonstrate that percent-level measurements of the fundamental mode and its overtones can be used to constrain the effective potential of tensor perturbations and the coupling functions between tensor modes and ones of different helicity, without assuming an underlying theory. We also apply our theory-agnostic reconstruction framework to analyze simulated quasi-normal mode data produced within specific theories extending general relativity, such as Chern-Simons gravity.