Quasinormal ringing of general spherically symmetric parametrized black holes

TL;DR

This paper investigates the quasinormal modes of parametrized black holes, demonstrating that dominant frequencies depend mainly on the first few parameters, thus providing a compact way to test strong gravity and constrain black-hole geometries.

Contribution

It extends the parametrization approach to quasinormal modes, showing that dominant frequencies are well determined by a few parameters for moderate black holes, aiding tests of gravity theories.

Findings

Dominant quasinormal modes depend mainly on the first few parameters.

Moderate black-hole geometries have predictable quasinormal frequencies.

Non-moderate geometries exhibit echoes and distinctive ringing not matching current data.

Abstract

The general parametrization of spherically symmetric and asymptotically flat black-hole spacetimes in arbitrary metric theories of gravity was suggested in [3]. The parametrization is based on the continued fraction expansion in terms of the compact radial coordinate and has superior convergence and strict hierarchy of parameters. It is known that some observable quantities, related to particle motion around the black hole, such as the eikonal quasinormal modes, radius of the shadow, frequency at the innermost stable circular orbit, and others, depend mostly on only a few of the lowest coefficients of the parametrization. Here we continue this approach by studying the dominant (low-lying) quasinormal modes for such generally parametrized black holes. We show that, due to the hierarchy of parameters, the dominant quasinormal frequencies are also well determined by only the first few coefficients of the expansion for the so-called moderate black-hole geometries. The latter are characterized by a relatively slow change of the metric functions in the radiation zone near the black hole. The nonmoderate metrics, which change strongly between the event horizon and the innermost stable circular orbit are usually characterized by echoes or by the distinctive (from the Einstein case) quasinormal ringing which does not match the current observational data. Therefore, the compact description of a black-hole spacetime in terms of the truncated general parametrization is an effective formalism for testing strong gravity and imposing constraints on allowed black-hole geometries.