Generalized Regge-Wheeler Equation from Effective Field Theory of Black Hole Perturbations with a Timelike Scalar Profile

TL;DR

This paper extends the effective field theory framework for scalar-tensor theories to include higher-order theories like DHOST, deriving a generalized Regge-Wheeler equation for black hole perturbations to analyze quasinormal modes.

Contribution

It generalizes the EFT-perturbation correspondence to higher-order scalar-tensor theories and derives a new master equation for black hole odd-parity perturbations.

Findings

Derived a generalized Regge-Wheeler equation for higher-order scalar-tensor theories.

Provided a framework to compute quasinormal modes and tidal Love numbers.

Extended EFT formalism to include DHOST and U-DHOST theories.

Abstract

Recently, the Effective Field Theory (EFT) of perturbations on an arbitrary background metric with a timelike scalar profile was formulated in the context of scalar-tensor theories. Here, we generalize the dictionary between the coefficients in the EFT action and those in covariant theories to accommodate shift- and reflection-symmetric quadratic higher-order scalar-tensor theories, including DHOST as well as U-DHOST. We then use the EFT action to study the dynamics of odd-parity perturbations on a static and spherically symmetric black hole background with a timelike scalar profile. Finally, we obtain the generalized Regge-Wheeler equation that can be used, e.g., to determine the spectrum of quasinormal modes and tidal Love numbers.