Effective Field Theory for the Perturbations of a Slowly Rotating Black Hole

TL;DR

This paper develops an effective theory framework for perturbations around scalar-haired and slowly rotating black holes, enabling efficient analysis and constraints on broad scalar-tensor theories, including parity-breaking effects.

Contribution

It introduces a unified effective theory for scalar-haired and slowly rotating black hole perturbations, incorporating galileon operators and parity-breaking effects.

Findings

Deformation of scalar-Gauss-Bonnet theory with galileon operators affects predictions.

Extension of the effective theory to axisymmetric, slowly rotating black holes at linear order in spin.

Framework facilitates constraining broad classes of scalar-tensor theories.

Abstract

We develop the effective theory for perturbations around black holes with scalar hair, in two directions. First, we show that the scalar-Gauss--Bonnet theory, often used as an example exhibiting scalar black hole hair, can be deformed by galileon operators leading to order unity changes to its predictions. The effective theory for perturbations thus provides an efficient framework for describing and constraining broad classes of scalar-tensor theories, of which the addition of galileon operators is an example. Second, we extend the effective theory to perturbations around an axisymmetric, slowly rotating black hole, at linear order in the black hole spin. We also discuss the inclusion of parity-breaking operators in the effective theory.