  Euler observers are a fundamental tool for the study of spacetime evolution.
Cauchy surfaces are evolved through the use of hypersurface orthogonal fields
and their relationship to coordinate observers, that enable the use of already
developed algorithms. In geometrodynamics new tetrad vectors have been
introduced with outstanding simplifying properties. We are going to use these
already introduced tetrad vectors in the case where we consider a curved four
dimensional Lorentzian spacetime with the presence of electromagnetic fields.
These Einstein-Maxwell geometries will provide the new tetrad that we are going
to use in order to develop an algorithm to produce Cauchy evolution with
additional simplifying properties.
