A new unified theory of electromagnetic and gravitational interactions

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 fivedimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: ▽_aF~(ab) - ξR_a~bA~a = —4πJ~b with ξ = —2, where Fab is the antisymmetric electromagnetic field tensor defined by the potential vector Aa, Rab 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 ξR_a~bA~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 Kaluza—Klein theory and its variants in which 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 certain 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.supported by the National Basic Research Program (973 Program) of China,the National Natural Science Foundation of China中国科学引文数据库(CSCD)6110402_01-110402_321