# naive covariantization

01 Nov 2023The classical Poisson-equation could me made relativistic by replacing the Laplace-operator and by using a 4-momentum density \(\jmath^\alpha\) as a source: \(\partial_i\partial^i\Phi = 4\pi G\rho \quad\rightarrow\quad \partial_\mu\partial^\mu A^\alpha = 4\pi G\jmath^\alpha\) Which phenomena would be correctly described and what would be a corresponding equation of motion in the gravitational field \(A^\alpha\)? what is fundamentally wrong with this “electrodynamics with masses”?

bonus question: What would be the Lagrange-density for the above field equation?