Scalar shortcut to beyond-Kerr ringdown tests and their complementarity with black-hole shadow observations

TL;DR

This paper introduces a scalar field-based method to estimate black hole quasinormal mode deviations from general relativity, providing a practical and accurate tool for testing gravity theories through ringdown and shadow observations.

Contribution

It proposes a novel approach using scalar quasinormal modes to approximate gravitational mode deviations, improving accuracy over traditional eikonal methods in certain regimes.

Findings

The method reproduces exact corrections within tens of percent for Kerr-Newman and Einstein-scalar-Gauss-Bonnet black holes.

Scalar quasinormal modes in phenomenological metrics are computed for the first time, revealing constraints comparable or superior to shadow observations.

Current ringdown measurements can effectively test gravity theories, with bounds that are often more stringent than those from black-hole shadow data.

Abstract

The quasinormal modes of black holes (BHs) in the large-angular-momentum limit can be computed within the eikonal approximation. This approximation is often extrapolated to low angular momentum to obtain a rough estimate of the dominant ringdown modes. Although approximate, this approach is particularly convenient in theories beyond general relativity with intricate dynamics, or for phenomenological metrics that lack an underlying fundamental theory. Here we explore a complementary approximate strategy: we compute exactly the quasinormal modes of a test scalar field propagating on the BH background and use their \emph{deviations} from the general-relativity predictions as a proxy for the corresponding corrections to the gravitational quasinormal modes. For Kerr-Newman and Einstein-scalar-Gauss-Bonnet BHs, we show that this method reproduces the exact corrections (including the coupling among different degrees of freedom) within tens of percent, an accuracy that is adequate as long as ringdown measurements remain at the percent level. Furthermore, this method is typically comparable to, or more accurate than, the eikonal approximation. We then apply the same strategy to phenomenological metrics commonly employed in tests of gravity using BH imaging. By computing scalar quasinormal modes in a large family of these metrics for the first time, we find that current ringdown constraints are comparable to, and in some cases more stringent than, those derived from BH shadow observations, while also providing complementary bounds on sectors that would otherwise be inaccessible.