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. Quasinormal modes of regular hairy black holes are calculated, and their thermodynamic properties are discussed. Both the Rényi and the Bekenstein-Hawking entropies are reported, deepening our understanding of gravitational dynamics in the strong-field regime, contributing to ongoing approaches to modified gravity.