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

It is shown that the equation of motion Duj/Ds = (e/mc2)Fjiui , 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 dxj ∂[jpi] = 0 or Lvpi = 0, where pi is the conjugate momentum 4-vector and v a vector determined by the condition pivi, 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.