On a relation between the Bach equation and the equation of geometrodynamics (Q1604930)

The condition that the Ricci tensor of a Weyl connection to \((g,A)\) vanishes, where \(g\) denotes a four-dimensional spacetime metric and \(A\) a vector field, is renamed by the authors ``equation of geometrodynamics''. They derive the Bach equation with the electromagnetic energy-momentum tensor to \(A\) on the right-hand side from it. Thus, an unexpected relation between second-order and fourth-order gravitational field equations is established.