Geodesics stability of Reissner–Nordström black hole spacetime

The study of geodesic motion provides a fundamental framework for probing the structure of spacetime and the nature of gravitational fields. In this work, we investigate the stability of geodesics in the Reissner–Nordström black hole spacetime, which represents a static, spherically symmetric solution of the Einstein–Maxwell field equations. Employing the Lyapunov stability approach, we analyze the stability properties of both timelike and null geodesics. The corresponding effective potentials are examined in detail, and the fixed points of the dynamical system are identified. We further explore the occurrence of saddle–node bifurcations and characterize the nature of geodesic motion near the fixed points using phase portraits. These results provide deeper insight into the dynamical behavior of massive and massless particles in the vicinity of charged black holes.