On the stability of cubic galileon accretion

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.

Hairy rotating black holes in cubic Galileon theory

“…where d is some fixed constant. Note here that the test field approximation (41) gives a wrong indication about the asymptotic behavior of Ψ (R) since it behaves as 1/ √ R although, according to equation (48), it behaves as 1/R 2 as soon as the coupling γ is nonzero, no matter how small. Yet this did not prevent the test-field solution from being useful as an initial guess in the numerical procedure.…”

“…On the theoretical side, various issues have been tackled within the framework of the cubic Galileon theory or larger theories including it: accretion onto a black hole [47,48], types of coupling to matter [49], laboratory tests [50], cosmological dynamics [51,52], structure formation [53], stability of cosmological perturbations [54,55], well-posedness [56][57][58][59]. Finally, it was found in [60] (with important precisions given in [61][62][63]) that shift-symmetric Horndeski theory along with the cubic Galileon is subject to a no-hair theorem in the static and spherically symmetric case (see also [64] for an extension to slow rotation and [65] for stars).…”