Maxwell-gravity

could one set up a relativistic (linear) theory of gravity that is analogous to Maxwell’s dynamics? the gravitational 4-potential \(A_\mu\) could be sourced through \(\Box A_\mu=4\pi G\jmath_\mu\) by a 4-momentum density \(\jmath_\mu\) which would be conserved, \(\partial^\mu\jmath_\mu=0\). what would be wrong with this idea, and which phenomena could be described?