  The problem of formulating synchronous variational principles in the context
of General Relativity is discussed. Based on the analogy with classical
relativistic particle dynamics, the existence of variational principles is
pointed out in relativistic classical field theory which are either
asynchronous or synchronous. The historical Einstein-Hilbert and Palatini
variational formulations are found to belong to the first category.
Nevertheless, it is shown that an alternative route exists which permits one to
cast these principles in terms of equivalent synchronous Lagrangian variational
formulations. The advantage is twofold. First, synchronous approaches allow one
to overcome the lack of gauge symmetry of the asynchronous principles. Second,
the property of manifest covariance of the theory is also restored at all
levels, including the symbolic Euler-Lagrange equations, with the variational
Lagrangian density being now identified with a $4-$scalar. As an application, a
joint synchronous variational principle holding both for the non-vacuum
Einstein and Maxwell equations is displayed, with the matter source being
described by means of a Vlasov kinetic treatment.
