  A general recipe proposed elsewhere to define, via Noether theorem, the
variation of energy for a natural field theory is applied to Einstein-Maxwell
theory. The electromagnetic field is analysed in the geometric framework of
natural bundles. Einstein-Maxwell theory turns then out to be natural rather
than gauge-natural. As a consequence of this assumption a correction term \a la
Regge-Teitelboim is needed to define the variation of energy, also for the pure
electromagnetic part of the Einstein-Maxwell Lagrangian. Integrability
conditions for the variational equation which defines the variation of energy
are analysed in relation with boundary conditions on physical data. As an
application the first law of thermodynamics for rigidly rotating horizons is
obtained.
