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.

黑洞是测试爱因斯坦广义相对论和其他引力理论的理想实验室。其中，爱因斯坦标量-高斯-邦尼理论近年来备受关注。根据标量场的耦合函数，产生的黑洞可能与广义相对论中的对应黑洞有很大不同。着眼于最低模式，针对几种类型的耦合函数解决了黑洞的线性模式稳定性。当除了与高斯-邦内项的耦合之外，还包含与曲率标量耦合的宇宙学驱动的进一步项时，就会出现一组新的不稳定性：球对称标量化黑洞的四极和十六极不稳定性，它们在径向扰动下是稳定的。