On a covariant Hamilton-Jacobi framework for the Einstein-Maxwell theory

The author extends the previously developed covariant Hamilton-Jacobi description of pure gravity in any dimension greater than two, to coupled electromagnetic and gravitational fields. In the case of pure gravity, the framework is based on a first-order differential equation on the bundle of metrics over spacetime manifold. In the case of coupled gravi- and electrodynamics, the abstract Hamilton-Jacobi equation is reduced naturally to a set of first-order equations on the bundle of metrics. Together with the result of the pure gravity theory claiming that the vanishing differential form of action is a complete integral of the Hamilton-Jacobi equation, this reduction indicates that the description of the Einstein-Maxwell theory is considerably simplified at the level of the covariant Hamilton-Jacobi framework.