  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. {\bf 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.
