On the Tetrad Formulation of the Equations of Motion in General Relativity

It is shown that the equation of motion Du_j/Ds = (e/mc²)F_jiuⁱ , a natural generalization to the curved spacetime of the Heaviside-Lorentz law of ponderomotive force, is equivalent to the metric independent and covariant Van Dantzig's equations of motion dx^j _[jpi] = 0 or L_vp_i = 0, where p_i is the conjugate momentum 4-vector and v a vector determined by the condition p_ivⁱ, only with respect to holonomic coordinates. With respect to an anholonomic system, the Heaviside-Lorentz equation is a particular case of the VD equations valid for a privileged class of anholonomic frames, those consisting of orthogonal unit vectors.