Volume 24, Nº 3 (2018)

We consider a natural form of a unified theory of gravity and electromagnetism which was somehow missed at the time of intense search for such a unification. The basic idea of this unification is to use the symmetric metric and a non-symmetric connection as independent variables, which generalizes the so-called Palatini formalism. For the first time this idea was applied to the construction of the action for a unified theory of gravity and electromagnetism without matter only in 1978, but this result did not receive wide recognition. In this paper we propose a natural way to include matter in the form of classical particles into the unified theory. The trace of connection in the appearing theory can be naturally identified with the electromagnetic potential, and the Einstein-Maxwell equations with classical matter are reproduced. We compare this approach with the known ideas of unification and briefly discuss the perspectives of a further development of this approach.

We consider a Fermion in the presence of a rotating BH immersed in a universe with a positive cosmological constant. After presenting a rigorous classification of the number and type of the horizons, we adopt the Carter tetrad to separate the aforementioned equation into radial and angular equations. We show how the Chandrasekhar ansatz leads to the construction of a symmetry operator that in the limit of a vanishing cosmological constant reproduces the square root of the squared total angular momentum operator for a Dirac particle in the Kerr metric. Furthermore, we prove that the the spectrum of the angular operator is discrete and consists of simple eigenvalues, and by means of the functional Bethe ansatz method we also derive a set of necessary and sufficient conditions for the angular operator to have polynomial solutions. Finally, we show that there exist no bound states for the Dirac equation in the non-extreme case.

One of the ways to describe string interaction with background fields is the sigma-model approach. Since free string theory is Weyl-invariant, it is demanded that the interacting string theory be Weyl-invariant as well. This leads to some equations on the background fields. As a result, such an approach allows in principle to derive the higher-spin equations of motion from string theory and therefore provides a bridge between string theory and field theory. In the present paper, we derive the equation of motion in the linear approximation for the simplest field with mixed symmetry of the indices.

A topologically nontrivial solution in Einstein-Dirac gravity with a cosmological constant is obtained. The space-time has the Hopf bundle as a spatial section. It is shown that the Hopf invariant is related to the spinor current density. Two Dirac spinors are used for obtaining a diagonal energy-momentum tensor. Solutions to the nongravitating Dirac equation in background Lorentzian space-time with the Hopf bundle as a spatial section are also obtained. Nongravitating solutions of the Dirac equation are characterized by two quantum half-integer numbers m, n.

As was shown recently, the scalar-tensor theory of gravitation proposed by Mbelek and Lachièze-Rey allows for a possible explanation of the forces reported in asymmetric microwave cavities. We show here that the theory in its revised version predicts a much simpler way of producing thrust by electrostatic means. We here briefly present the equations and derivations indicating that a constant force is predicted for a spherical capacitor with an asymmetric mass distribution, kept at constant voltage. Apart form other practical implications, this particular prediction, and a complementary proposal in which the spherical capacitor takes the place of the large mass in a Cavendish-like experiment, provides an additional possibility of experimentally testing this particular scalar-tensor gravitational theory.

We study Holographic dark energy in 5D Brans-Dicke cosmology. To investigate the stability and attractor solutions, we fit the model with the SNIa and Gamma-Ray Burst (GRB) observational data. We also examine the holographic nature of dark energy in the model through the equation of state (EoS). In addition, a reconstructed form of the EoS from holographic dark energy on the model is driven The model strongly exhibits the present cosmic accelerating. It also shows that the universe starts from an unstable radiation-dominated epoch and reaches a stable late-time accelerated phase originating from holographic dark energy in the Brans-Dicke model.