On the Stability of Cubic Galileon Accretion

TL;DR

This paper investigates the linear stability of steady-state cubic galileon scalar field accretion onto a Schwarzschild black hole, establishing conditions for stability through perturbation analysis and effective metric construction.

Contribution

It provides the first detailed stability analysis of cubic galileon accretion in a Schwarzschild background, including the derivation of the effective metric and sonic horizon.

Findings

The accretion solution is linearly stable.

The effective metric governs the propagation of fluctuations.

The sonic horizon is identified and matched across branches.

Abstract

We examine the stability of steady-state galileon accretion for the case of a Schwarzshild black hole. Considering the galileon action up to the cubic term in a static and spherically symmetric background we obtain the general solution for the equation of motion which is divided in two branches. By perturbing this solution we define an effective metric which determines the propagation of fluctuations. In this general picture we establish the position of the sonic horizon together with the matching condition of the two branches on it. Restricting to the case of a Schwarzschild background, we show, via the analysis of the energy of the perturbations and its time derivative, that the accreting field is linearly stable.