The field equations for gravitation and electromagnetism

Abstract

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 field gμν itself.
Conclusion: The theory of gravitation and electromagnetism of Einstein and Maxwell are unified and described exclusively in terms of the
metric tensor gμν