Gravitational decoupling and regular hairy black holes: Geodesic stability, quasinormal modes, and thermodynamic properties

The stability of geodesic orbits around a regular hairy black hole, in the gravitational decoupling setup, is investigated by employing Lyapunov exponents, which quantify the divergence rate of nearby trajectories in dynamical systems. Both timelike and null geodesics are addressed, probing the effect of the hair parameter on orbital stability. Deviations from the Schwarzschild solution have a significant influence on orbit stability, potentially providing observational signatures. We compute the quasinormal modes of regular hairy black holes and discuss their thermodynamic properties, contrasting the Rényi and Bekenstein-Hawking entropy prescriptions. The results can provide insight into gravitational dynamics in the strong-field regime and potentially contribute to ongoing developments in modified gravity theories.