Effective Field Theory of Black Hole Quasinormal Modes in Scalar-Tensor Theories

TL;DR

This paper develops an effective field theory framework to analyze black hole quasinormal modes in scalar-tensor theories, enabling model-independent predictions of how scalar hair influences gravitational wave signals during ringdown.

Contribution

It introduces an effective description for perturbations in scalar-tensor theories and applies a light ring expansion to express quasinormal modes in terms of few parameters.

Findings

Scalar hair can shift the quasinormal spectrum.

Breaking of isospectrality between polar and axial modes.

Potential scalar radiation signatures.

Abstract

The final ringdown phase in a coalescence process is a valuable laboratory to test General Relativity and potentially constrain additional degrees of freedom in the gravitational sector. We introduce here an effective description for perturbations around spherically symmetric spacetimes in the context of scalar-tensor theories, which we apply to study quasi-normal modes for black holes with scalar hair. We derive the equations of motion governing the dynamics of both the polar and the axial modes in terms of the coefficients of the effective theory. Assuming the deviation of the background from Schwarzschild is small, we use the WKB method to introduce the notion of "light ring expansion". This approximation is analogous to the slow-roll expansion used for inflation, and it allows us to express the quasinormal mode spectrum in terms of a small number of parameters. This work is a first step in describing, in a model independent way, how the scalar hair can affect the ringdown stage and leave signatures on the emitted gravitational wave signal. Potential signatures include the shifting of the quasi-normal spectrum, the breaking of isospectrality between polar and axial modes, and the existence of scalar radiation.