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In this paper we will review some facts, both classical and recent, concerning the geometry and analysis of the Kerr and related black hole spacetimes. This includes the analysis of test fields on these spacetimes. Central to our analysis…

The Dirac monopole string is specified for de Sitter cosmological model. Dirac equation for spin 1/2 particle in presence of this monopole has been examined on the background of de Sitter space-time in static coordinates. Instead of spinor…

We review a technique for solving a class of classical linear partial differential systems of relevance to physics in Minkowski spacetime. All the equations are amenable to analysis in terms of complex solutions in the kernel of the scalar…

On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi}) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor…

The new spinor-unit field representation of the electromagnetism \cite{Nash2010} (with quark and lepton sources) is integrated via minimal coupling with standard Einstein gravitation, to formulate a Lagrangian model of the very early…

Spinor fields on surfaces of revolution conformally immersed into 3-dimensional space are considered in the framework of the spinor representations of surfaces. It is shown that a linear problem (a 2-dimensional Dirac equation) related with…

We obtain solutions of the Klein-Gordon and Dirac equations in the gravitational fields of vacuumless defects. We calculate the energy levels and the current, respectively, in the scalar and spinor cases. In all these situations we…

The existence of Kerr-Dold-type vortices in axisymmetric stagnation point flow is demonstrated, extending the class of known thick vortex solutions.

The gravity-capillary problem with inclined walls is a problem that describes an open fluid flowing over an angled wall. It has broad applications in science and engineering. In this paper, we study the steady states of the two-dimensional…

This paper encompasses a set of stellar equations that administer the formation and evolution of self-gravitating, dissipative spherically symmetric fluid distributions having anisotropic stresses in the presence of electromagnetic field.…

We consider an extended version of the Kerr theorem incorporated in the Kerr-Schild formalism. It allows one to construct the series of exact solutions of the Einstein-Maxwell field equations from a holomorphic generating function $F$ of…

We show that all domain-wall solutions of gravity coupled to scalar fields for which the worldvolume geometry is Minkowski or anti-de Sitter admit Killing spinors, and satisfy corresponding first-order equations involving a superpotential…

The rapid experimental progress of ultra-cold dipolar fermions opens up a whole new opportunity to investigate novel many-body physics of fermions. In this article, we review theoretical studies of the Fermi liquid theory and Cooper pairing…

In this work we have found an exact solution for the problem of the movement of a dipole type point vortex in an area of fluid limited by a flat boundary. We also present a solution to the problem of dipole point vortex motion in a right…

A common view is that generalization of a wave equation on Riemannian space-time is substantially determined by what a particle is - boson or fermion. As a rule, they say that tensor equations for bosons are extended in a simpler way then…

In this paper, we study the Dirac equation for an electron constrained to move on a catenoid surface. We decoupled the two components of the spinor and obtained two Klein-Gordon-like equations. Analytical solutions were obtained using…

We study collective excitations in a helical electron liquid on a surface of three-dimensional topological insulator. Electron in helical liquid obeys Dirac-like equation for massless particless and direction of its spin is strictly…

The dynamics of a spinning fluid in a flat cosmological model is investigated. The space-time is itself generated by the spinning fluid which is characterized by an energy-momentum tensor consisting a sum of the usual perfect-fluid…

There are two different methods to describe membrane (string) fluids, which use different field content. The relation between the methods is clarified by construction of combined method. Dirac membrane field appears naturally in new…

Different characteristic of matter influencing the evolution of the Universe has been simulated by means of a nonlinear spinor field. We have considered two cases where the spinor field nonlinearity occurs either as a result of self-action…