We discuss a dynamical systems approach to prove the existence of a Lorentzian spacetime that is the solution of the Einstein field equations coupled with an electric field obeying the equations of Maxwell-Bopp-Lande-Thomas-Podolsky for a static point charge. This is a law of electromagnetism proposed in the 1940's that generalizes the usual Maxwell equations and which, in the Minkowski space of Special Relativity, solves the problem of the infinite self-energy of the field generated by a particle. We show that it also solves the same problem in our general relativistic context, which will permit future investigations such as the joint problem for the time evolution of point charges and their electromagnetic fields.