RADIAL STABILITY OF SPHERICALLY SYMMETRIC BLACK HOLES IN SCALAR-TENSOR GRAVITY COUPLED TO NONLINEAR ELECTRODYNAMICS

Abstract

We investigate the radial stability of asymptotically flat, spherically symmetric black hole solutions in scalar-tensor gravity coupled to nonlinear electrodynamics (NED). The inclusion of the NED sector bypasses standard scalar no-hair theorems, providing a rigorous mechanism for the existence of horizons with non-trivial scalar profiles. By considering time-dependent monopole ( ) perturbations, we derive the fully coupled linearized equations governing the gravitational and scalar fields. Recognizing that electromagnetic perturbations do not introduce independent dynamical degrees of freedom in the monopole sector, we utilize a gauge-invariant framework to decouple the system into a single master wave equation governed by a scalar effective potential. The stability of the static background is analyzed through the properties of this effective potential. In parameter regions where the potential exhibits negative wells, we strictly apply the S-deformation method to rule out the existence of unstable normalizable bound states. Our analytical results establish the exact parametric bounds required for the radial stability of these configurations, demonstrating that stability is rigidly constrained by the NED coupling parameter and the effective scalar charge.