Nonlinear Stability of Black Holes with a Stable Light Ring

Recently, ultracompact objects have been found to be susceptible to a new nonlinear instability, known as the light-ring instability, triggered by stable light rings. This discovery raises concerns about the viability of these objects as alternatives to black holes. In this work, we investigate the presence of the light-ring instability in scalarized Reissner-Nordstr\"om black holes, which have been previously shown to admit stable light rings. We employ fully nonlinear numerical evolutions of both scalarized black holes with and without stable light rings, perturbing them initially with spherically symmetric scalar perturbations. Our simulations demonstrate the long-term stability of these scalarized black holes, suggesting that the presence of a stable light ring may not necessarily induce the light-ring instability.