Effective potential U_eff given by Eq. (C.19) for selected values of the conserved angular momentum L. Left: massive BH case, i.e., Schwarzschild solution, g₀₀ = 1 − 2M/r. Right: DM case; g₀₀ obtained from numerical integration of the general relativistic equilibrium equations of the extended RAR model for a fermion mass mc² = 56 keV, see Appendix A for details. Imposing a bound orbit within given values of the pericenter and apocenter (vertical dashed lines), in this example, r_p/M = 2.976 × 10³ and r_a/M = 4.714 × 10⁴, respectively, implies a unique solution of E (dashed horizontal value) and L (value associated with the blue curve). In this example, the adopted mass of the massive BH for the Schwarzschild solution is M_BH ≡ M = 4.075 × 10⁶ M_⊙, and for the mass of the DM RAR core, it was set to M_c = 3.5 × 10⁶ M_⊙.