Ringdowns for black holes with scalar hair: the large mass case

TL;DR

This paper develops an effective field theory approach to analyze black hole ringdowns with scalar hair, showing that deviations from Kerr are heavily suppressed for large black holes, making detection unlikely with LISA.

Contribution

It introduces a perturbative framework for calculating QNMs of black holes with scalar hair, extending the analysis to second order and assessing observational prospects.

Findings

Corrections to QNM frequencies are suppressed for large black holes.

LISA is unlikely to detect scalar hair in ringdown signals.

A systematic perturbative method for QNMs with scalar hair is developed.

Abstract

Deviations from General Relativity can alter the quasi-normal mode (QNM) ringdown of perturbed black holes. It is known that a shift-symmetric (hence massless) scalar can only introduce black hole hair if it couples to the Gauss-Bonnet invariant, in which case the scalar charge is fixed with respect to the black hole mass and controlled by the strength of that coupling. The charge per unit mass decreases with the mass and can, therefore, be used as a perturbative parameter for black holes that are sufficiently large with respect to the scale suppressing the deviation from General Relativity or the Standard model. We construct an effective field theory scheme for QNMs using this perturbative parameter to capture deviations from Kerr for both the background and the perturbations. We demonstrate that up to second order in the charge per unit mass, QNMs can be calculated by solving standard linearised perturbation equations for the Kerr metric with sources depending on solutions of the same equations up to first order. It follows that corrections to the QNM frequencies are heavily suppressed for sufficiently massive black holes, meaning that LISA is very unlikely to detect any evidence of scalar hair in ringdown signals.