  In this work, the dynamic of isolated systems in general relativity is
described when gravitational radiation and electromagnetic fields are present.
In this construction, the asymptotic fields received at null infinity together
with the regularized null cone cuts equation, and the center of mass of an
asymptotically flat Einstein-Maxwell spacetime are used. A set of equations are
derived in the low speed regime, linking their time evolution to the emitted
gravitational radiation and to the Maxwell fields received at infinity. These
equations should be useful when describing the dynamic of compact sources, such
as the final moments of binary coalescence and the evolution of the final black
hole. Additionally, we compare our equations with those coming from a similar
approach given by Newman, finding some differences in the motion of the center
of mass and spin of the gravitational system.
