We prove the stability of the critical hypersurfaces associated with the three-dimensional general relativistic Poynting-Robertson effect. The equatorial ring configures to be as a stable attractor and the whole critical hypersurface as a basin of attraction for this dynamical system. We introduce a new, simpler (in terms of calculations), and more physical approach within the Lyapunov theory. We propose three different Lyapunov functions, each one carrying important information and very useful for understanding such phenomenon under different aspects.