The field equations for gravitation and electromagnetism

Aim: The development of a unified field theory for electromagnetism and gravitation while no material source terms are taken into  account in the field equations of unified field theory is still an issue to be solved.
Methods: The usual tensor calculus rules were used.
Results: The gravitational and the electromagnetic field are successfully joined into one single hyper-field whose equations are determined only by the metric tensor of general relativity g_mn itself.
Conclusion: The theory of gravitation and electromagnetism of Einstein and Maxwell are unified and described exclusively in terms of the metric tensor g_mn.