In this paper we present a new unified theory of electromagnetic and gravitational interactions .
By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime , we derive the complete set of field equations in the four-dimensional spacetime from the five-dimensional Einstein field equation .
Besides the Einstein field equation in the four-dimensional spacetime , an electromagnetic field equation is derived : \nabla _ { a } F ^ { ab } - \xi R ^ { b } _ { a } A ^ { a } = -4 \pi J ^ { b } with \xi = -2 , where F ^ { ab } is the antisymmetric electromagnetic field tensor defined by the potential vector A ^ { a } , R _ { ab } is the Ricci curvature tensor of the hypersurface , and J ^ { a } is the electric current density vector .
The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term \xi R ^ { b } _ { a } A ^ { a } , whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge as discussed in a previous paper by the author [ L.-X .
Li , Gen. Relativ .
Gravit . 48 , 28 ( 2016 ) ] .
Hence , the new unified theory is physically different from the Kaluza-Klein theory and its variants where the Einstein-Maxwell equation is derived .
In the four-dimensional Einstein field equation derived in the new theory , the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter .
Under some conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime .
We argue that , the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density , e.g. , inside a neutron star or a white dwarf , and in the early epoch of the universe .

KEY WORDS : General relativity , Maxwell ’ s equations , unified theory , Kaluza-Klein theory , brane world theory