A new unified theory of electromagnetic and gravitational interactions

作     者：Li-Xin Li 

作者机构：Kavli Institute for Astronomy and Astrophysics Peking University Beijing 100871 China 

出 版 物：《Frontiers of physics》 (物理学前沿（英文版）)

年 卷 期：2016年第11卷第6期

页      面：35-66页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：supported by the National Basic Research Program (973 Program) of China 国家自然科学基金 

主　　题：general relativity Maxwell's equations unified field theory Kaluza-Klein theory brane world theory 

摘      要：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 obtained: del F-a(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 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.