Different Lorentz factor profiles: The profile derived in Falcke (1996) and used in agnjet cf. Markoff et al. (2005, yellow solid line), the profile derived in this work after correcting algebraic errors (Eq. ( 18), red solid line), and the profiles found by solving the 1D Euler equation of a conical jet assuming the gas is isothermal (green dashed line) and adiabatic (lilac solid line). If the jet follows Bernoulli’s equation, γ_maxβ_max ≈ 2.39 when γ₀β₀ ≈ 0.485 and Γ = 4 / 3-precisely the terminal value in the adiabatic jet Lorentz factor profile.