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

Giovanni D’Addario1,2,3, Antonio Padilla2,3, Paul M. Saffin2,3, Thomas P. Sotiriou1,2,3, and Andrew Spiers1,3

  • 1School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
  • 2School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
  • 3Nottingham Centre of Gravity, Nottingham NG7 2RD, United Kingdom

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Phys. Rev. D 109, 084046 – Published 18 April, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.084046

Abstract

Deviations from general relativity can alter the quasinormal 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 linearized 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.

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Phys. Rev. D 109, 084046– Published 18 April, 2024
  • Received 18 December 2023
  • Accepted 13 March 2024
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