Radial perturbations of scalar-Gauss-Bonnet black holes beyond spontaneous scalarization

Understand

Spontaneous scalarization of black holes in scalar-Gauss-Bonnet (sGB) gravity is a very interesting phenomenon allowing black holes to circumvent the no-hair theorem and acquire scalar hair while leaving the weak field regime of the theory practically unaltered.

• It was recently shown that if we allow for a different form of the coupling between the scalar field and the Gauss-Bonnet invariant, a new type of scalarization is possible beyond the standard one that can be excited only nonlinearly.
• In this case the spectrum of black hole solutions can be more complicated, naturally opening the question about their stability.
• The goal of the present paper is to study this question including the possible loss of hyperbolicity of the radial perturbation equation.