Quasi-Normal Modes of Hairy Scalar Tensor Black Holes: Odd Parity

TL;DR

This paper analyzes the odd parity gravitational Quasi-Normal Modes of black holes with scalar hair in Horndeski gravity, providing a modified equation and parameterization for small deviations from Schwarzschild black holes.

Contribution

It introduces a quadratic order modified Regge-Wheeler equation for hairy black holes and estimates the statistical errors of the new parameters.

Findings

Derived a modified Regge-Wheeler equation for hairy black holes.

Provided a parameterization of the Quasi-Normal Mode spectrum.

Estimated statistical errors for the hairy parameters.

Abstract

The odd parity gravitational Quasi-Normal Mode spectrum of black holes with non-trivial scalar hair in Horndeski gravity is investigated. We study `almost' Schwarzschild black holes such that any modifications to the spacetime geometry (including the scalar field profile) are treated as small quantities. A modified Regge-Wheeler style equation for the odd parity gravitational degree of freedom is presented to quadratic order in the scalar hair and spacetime modifications, and a parameterisation of the modified Quasi-Normal Mode spectrum is calculated. In addition, statistical error estimates for the new hairy parameters of the black hole and scalar field are given.