(plenary invited speaker)

Instabilities of Black Holes in Einstein-Scalar-Gauss-Bonnet Theories

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.