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 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.Comment: 41 pages, including 1 figure and 1 table. A new section is added to describe the relation to the Kaluza-Klein theory. Version accepted to Frontiers of Physic

Variation of the Amati Relation with the Cosmological Redshift: a Selection Effect or an Evolution Effect?

Because of the limit in the number of gamma-ray bursts (GRBs) with available redshifts and spectra, all current investigations on the correlation among GRB variables use burst samples with redshifts that span a very large range. The evolution and selection effects have thus been ignored, which might have important influence on the results. In this Letter, we divide the 48 long-duration GRBs in Amati (2006, 2007) into four groups with redshift from low to high, each group contains 12 GRBs. Then we fit each group with the Amati relation \log E_\iso = a + b \log E_\p, and check if the parameters $a$ and $b$ evolve with the GRB redshift. We find that $a$ and $b$ vary with the mean redshift of the GRBs in each group systematically and significantly. Monte-Carlo simulations show that there is only $\sim 4$ percent of chance that the variation is caused by the selection effect arising from the fluence limit. Hence, our results may indicate that GRBs evolve strongly with the cosmological redshift.Comment: 5 pages, including 5 figures. MNRAS Letters accepte

Nuclearity of semigroup C*-algebras and the connection to amenability

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*-algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full corners in associated group crossed products. These descriptions allow us to characterize nuclearity of semigroup C*-algebras in terms of faithfulness of left regular representations and amenability of group actions. Moreover, we also determine when boundary quotients of semigroup C*-algebras are UCT Kirchberg algebras. This leads to a unified approach to Cuntz algebras and ring C*-algebras.Comment: 42 pages; revised version, corrected typo

K-theory for ring C*-algebras attached to function fields with only one infinite place

We study the K-theory of ring C*-algebras associated to rings of integers in global function fields with only one single infinite place. First, we compute the torsion-free part of the K-groups of these ring C*-algebras. Secondly, we show that, under a certain primeness condition, the torsion part of K-theory determines the inertia degrees at infinity of our function fields.Comment: 27 page