Radial perturbations of the scalarized Einstein-Gauss-Bonnet black holes

Abstract

Recently a new class of scalarized black holes in Einstein-Gauss-Bonnet (EGB) theories was discovered. What is special for these black hole solutions is that the scalarization is not due to the presence of matter, but it is induced by the curvature of spacetime itself. Moreover, more than one branch of scalarized solutions can bifurcate from the Schwarzschild branch, and these scalarized branches are characterized by the number of nodes of the scalar field. The next step is to consider the linear stability of these solutions, which is particularly important due to the fact that the Schwarzschild black holes lose stability at the first point of bifurcation. Therefore we here study in detail the radial perturbations of the scalarized EGB black holes. The results show that all branches with a nontrivial scalar field with one or more nodes are unstable. The stability of the solutions on the fundamental branch, whose scalar field has no radial nodes, depends on the particular choice of the coupling function between the scalar field and the Gauss-Bonnet invariant. We consider two particular cases based on the previous studies of the background solutions. If this coupling has the form used in [1] the fundamental branch of solutions is stable, except for very small masses. In the case of a coupling function quadratic in the scalar field [2], though, the whole fundamental branch is unstable.

Spinning and excited black holes in Einstein-scalar-Gauss–Bonnet theory

“…Before we turn to rotating black holes, let us briefly recall the properties of static black holes in this theory [25,28]. The bifurcation points of the sets of static scalarized black holes from the branch of Schwarzschild black holes have been obtained for the quadratic coupling function in [25], and they agree with those of the exponential coupling [24], since the latter reduces to the quadratic coupling in the limit of small scalar field.…”

“…While we do not expect stable spontaneously scalarized black holes for this theory, it should be possible to restore stability by adding higher-order terms to the coupling function [24,28] or by including a potential term V (φ) for the scalar field [31,49]. The latter approach is particularly attractive, since these corrections would emerge naturally in an effective field theory scenario.…”

“…Later it was realized that spontaneous scalarization can occur for charged black holes in Einstein-Maxwell-scalar (EMs) theory, for certain choices of the scalar coupling function and coupling strength [36][37][38][39][40][41]. This "charge-induced" spontaneous scalarization presents many similarities with the case of curvature-induced spontaneous scalarization of black holes [24][25][26][27][28][29][30][31][32].…”

Scalarization of horizonless reflecting stars: Neutral scalar fields non-minimally coupled to Maxwell fields

“…This intriguing mechanism of hair formations is usually called spontaneous scalarization. At present, lots of spontaneous scalarization models were constructed in the background of black holes [51][52][53][54][55][56][57][58][59][60].…”

Black hole spontaneous scalarisation with a positive cosmological constant

“…As a result, the GR solutions are unstable against scalar perturbations in regions where the source term is significant, dynamically developing scalar hair, i.e. spontaneously scalarising.Various expressions of I have been considered in the literature, that fall roughly into two types: I is a geometric invariant, such as the Gauss-Bonnet invariant [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], the Ricci scalar for non-conformally invariant BHs [37], or the Chern-Simons invariant [38]; or I is a "matter" invariant, such as the Maxwell F 2 term [39][40][41][42][43][44][45][46]. This phenomenon is actually not exclusive of scalar fields [47].…”