Abstract
Black holes represent an ideal laboratory to test Einstein’s theory of general relativity and alternative theories of gravity. Among the latter, Einstein-scalar–Gauss–Bonnet Theories have received much attention in recent years. Depending on the coupling function of the scalar field, the resulting black holes may then differ significantly from their counterparts in general relativity. Focusing on the lowest modes, linear mode stability of the black holes is addressed for several types of coupling functions. When in addition to the coupling to the Gauss–Bonnet term a cosmologically motivated further term with coupling to the curvature scalar is included, a new set of instabilities arises: quadrupole and hexadecupole instabilities of spherically symmetric scalarized black holes, that are stable under radial perturbations.
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