Stealth black hole perturbations in kinetic gravity braiding

TL;DR

This paper investigates perturbations of stealth black holes in kinetic gravity braiding, deriving master equations and analyzing the nature of monopolar and dipolar modes, revealing their pathological or gauge nature.

Contribution

It derives the Regge-Wheeler and Zerilli master equations for stealth black holes in kinetic gravity braiding and analyzes the physical nature of low-order perturbations.

Findings

Stealth black hole perturbations are governed by modified master equations.

Monopolar and dipolar perturbations are either non-physical or gauge modes.

Additional hair contributes only an extra source term to the even parity equation.

Abstract

We study stealth black hole perturbations in shift symmetric kinetic gravity braiding and obtain its analogous Regge-Wheeler and Zerilli master equations for the odd and even parity sectors. We show that the nontrivial hair of static and spherically symmetric stealth black holes contributes only an additional source term to the even parity master equation. Furthermore, we derive exact solutions to the monopolar and dipolar perturbations and show that they are generally pathological non-gauge modes, or else reduce to the pure-gauge low-order multipoles of general relativity.