Some new radiating Kerr-Newman solutions

Three exact non-static solutions of Einstein-Maxwell equations corresponding to a field of flowing null radiation plus an electromagnetic field are presented. These solutions are non-static generalizations of the well known Kerr-Newman solution. The current vector is null in all the three solutions. These solutions are the electromagnetic generalizations of the three generalized radiating Kerr solutions discussed by Vaidya and Patel. The solutions discussed by us describe the exterior gravitational fields of rotating radiating charged bodies. Many known solutions are derived as particular cases.     

A class of homogeneous cosmological models

Einstein's field equations are studied under the assumptions that (1) the source of the gravitational field is a perfect fluid, and (2) there exists a group of motions simply transitive on three-surfaces orthogonal to the fluid flow vector. There are two classes of solutions; these are studied in detail. Three special families of solutions examined include all analytic solutions of the field equations obeying (1) and (2) of which the authors are aware. The relation of these solutions to various vacuum solutions is indicated.     

Rotating viscous-fluid cosmologies with scalar field and heat flux

Rotating cosmological models under the influence of both shear and bulk viscosity, together with scalar field and heat flow, are studied. Exact solutions of the field equations are obtained. The solutions have nonzero expansion, shear, and rotation. The properties of the solutions are studied and the temperature distribution is also given explicitly.     

沿直线分布电荷体系电场线的解析解

通过求解电场线所满足的微分方程,得到了沿直线分布电荷体系电场线的严格解析解,根据所得电场线簇方程,讨论了各种沿直线分布电荷体系的电场线特点,并在计算机上利用Mathematica软件绘出了相应的电场线分布图.     

Scalar field solutions to Yang-Mills and Vierbein field theories

Covariant solutions to the Vierbein (gravitational) field equations are related to solutions of scalar field equations. New solutions to the latter are also given.     

Yang-Mills cosmologies and collapsing gravitational sphalerons

Cosmological solutions with a homogeneous Yang-Mills field which oscillates and passes between topologically distinct vacua are discussed. These solutions are used to model the collapsing Bartnik-McKinnon gravitational sphaleron and the associated anomalous production of fermions. The Dirac equation is analyzed in these backgrounds. It is shown explicity that a fermion energy level crosses from the negative to positive energy spectrum as the gauge field evolves between the topologically distinct vacua. The cosmological solutions are also generalized to include an axion field.     

A generalized field theory

Three solutions with spherical symmetry are obtained for the field equations of the generalized field theory established recently by Mikhail and Wanas. The solutions found are in agreement with classical known results. The solution representing a generalized field, outside a spherical symmetric charged body, is found to have an extra term compared with the Reissner-Nordström metric. The space used for application is of type FIGI, so the solutions obtained correspond to a field in a matter-free space. A brief comparison between the solutions obtained and those given by other field theories is given. Two methods have been used to get physical results: the first is the type analysis, and the second is the comparison with classical known results by writing down the metric of the associated Riemannian space.     

The equivalence of perfect fluid space-times and viscous magnetohydrodynamic space-times in general relativity

The work of a previous article [1] is extended to show that space-times which are the exact solutions of the field equations for a perfect fluid also may be exact solutions of the field equations for a viscous magnetohydrodynamic fluid. Conditions are found for this equivalence to exist and viscous magnetohydrodynamic solutions are found for a number of known perfect fluid space-times.     

Thermodynamic properties of the XX model in a chain with a period two and three coupling

The exact solutions for the energy spectrum of the XX model with a periodic coupling and an external transverse magnetic field h are obtained. The diagonalization procedure is discussed, and analytical and numerical solutions are given. Using the solutions for period-two coupling, the free energy, entropy, and specific heat are calculated as functions of temperature and applied transverse external magnetic field. Their expressions show that below a particular value v and above a value u of the magnetic field |h|, the entropy and the specific heat vanish exponentially in the low temperature limit.     

Euclidean Wormholes with Phantom Field and Phantom Field Accompanied by Perfect Fluid

We study the classical Euclidean wormhole solutions for the gravitational systems with minimally coupled pure Phantom field and minimally coupled Phantom field accompanied by perfect fluid. It is shown that such solutions do exist and then the general forms of the Phantom field potential are obtained for which there are classical Euclidean wormhole solutions.     

Einstein-Yang-Mills-Higgs solitons

The classical theory of the gravitational field coupled to an SO(3) gauge field and to a ghost Higgs field in (3+1) dimensions is found to admit regular localized solutions of the electric or magnetic type. These solutions, which generalize solutions previously found for the Abelian case, are characterized by a non-Euclidean spatial topology, with two points at infinity.     

Kundt solutions of Einstein's equations with one non-null Killing vector

The Kundt class of algebraically special solutions of Einstein's field equations, representing vacuum and electromagnetic null fields with one twisting, non-null Killing vector, is discussed. This generalizes the case with a hypersurface-orthogonal Killing vector field which is discussed by Kramer and Neugebauer [3]. The solutions are shown to be equivalent to the Hoenselaers (vacuum) and Hoenselaers-Skea (electromagnetic null) solutions, once some small corrections and the relevant coordinate transformations are made to the latter solutions.     

A Modified Gravity Theory: Null Aether

General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the "aether". In this paper, we put forward the idea of a null aether field and introduce, for the first time, the Null Aether Theory(NAT) — a vector-tensor theory. We first study the Newtonian limit of this theory and then construct exact spherically symmetric black hole solutions in the theory in four dimensions, which contain Vaidya-type non-static solutions and static Schwarzschild-(A)dS type solutions, Reissner-Nordstr?m-(A)dS type solutions and solutions of conformal gravity as special cases. Afterwards, we study the cosmological solutions in NAT:We find some exact solutions with perfect fluid distribution for spatially flat FLRW metric and null aether propagating along the x direction. We observe that there are solutions in which the universe has big-bang singularity and null field diminishes asymptotically. We also study exact gravitational wave solutions — AdS-plane waves and pp-waves — in this theory in any dimension D ≥ 3. Assuming the Kerr-Schild-Kundt class of metrics for such solutions, we show that the full field equations of the theory are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. The main conclusion of these computations is that the spin-0 aether field acquires a "mass" determined by the cosmological constant of the background spacetime and the Lagrange multiplier given in the theory.     

Supersymmetric 3D anti-de Sitter space solutions of type IIB supergravity

For every positively curved K?hler-Einstein manifold in four dimensions, we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of AdS3 with a compact seven-dimensional manifold and have nonvanishing five-form flux. Via the anti-de Sitter/conformal field theory correspondence, the solutions are dual to two-dimensional conformal field theories with (0,2) supersymmetry. The corresponding central charges are rational numbers.     

Classical pion fields in the presence of a source

A classical pion field that is similar to a disoriented chiral condensate is considered in the presence of an external source. The field is similar to the condensate in that the isotopic orientation of the field in the whole space is determined by a single vector. Within the nonlinear sigma model, classical solutions are considered both in the chiral limit, where the pions are massless, and in the case of a finite pion mass. In either case, the classical filed is similar to the Coulomb field of a charged particle; however, the nonlinear pion interaction results in the existence of several solutions. In the massless case and in the case where the source is sufficiently small, there are a great number of classical solutions characterized by finite discrete energies. In the more realistic case of heavy ions, there are no stable solutions of this type; however, long-lived quasistationary states, which slowly decay, emitting very soft pions, can be formed. The structure and the energies of these solutions are studied numerically.     

Higher dimensional Vaidya metric in Einstein and de Sitter background

Spherically symmetric non-static higher dimensional metrics are considered in connection with Einstein’s field equations. Two exact solutions are derived. One of them corresponds to a mixture of perfect fluid and pure radiation field and represents higher dimensional Vaidya metric in the cosmological background of Einstein static universe. The other corresponds to a pure radiation field and represents higher dimensional Vaidya metric in the background de Sitter universe. For both of these solutions, the cosmological constant is taken to be non-zero. Many known solutions are derived as particular cases.     

Equilibrium configurations of uncharged conducting liquid jets in a transverse electric field

Solutions for the problem on the equilibrium configurations of uncharged conducting liquid jets in a transverse electric field are obtained. These solutions correspond to finite-amplitude non-axisymmetric azimuthal deformations of the surface of a round jet: the jet is stretched along the field in its cross-section. The range of electric fields is determined for which solutions of the problem exist. If the electric field strength is over some critical value, the electrostatic equations have no solution, and the jet splits. The obtained solutions are qualitatively examined for stability under small azimuthal perturbations.     

Cylindrically symmetric Brans-Dicke fields. I

A class of rigorous solutions for the Brans-Dicke scalar-tensor theory for Einstein-Rosen nonstatic cylindrically symmetric metric is obtained when only scalar field is present (vacuum solutions of Brans-Dicke theory). As the solutions of Brans-Dicke vacuum fields are conformal to either zero-mass scalar field or vacuum solutions of Einstein's gravitational theory, a set of solutions conformal to the above which correspond to zero-mass scalar field has also been obtained.     

The Maxwell Group and the Quantum Theory of Particles in Classical Homogeneous Electromagnetic Fields

Covariant solutions of the Dirac (and Klein-Gordon) equation in a homogeneous classical electromagnetic field are constructed. This is done using the symmetry group of the equation, the Maxwell group. These covariant solutions are obtained starting from solutions in the frame where the electromagnetic field is described by a magnetic field pointing in the 3-direction and then using the theory of induced representations.     

Gravitational fields with groups of motions on two-dimensional transitivity hypersurfaces in a model with matter and a magnetic field

For gravitational fields with metrics which admit of groups of motions multiply — transitive on 2-dimensional space-like invariant varieties, the exact solutions of the Einstein gravitational equations are given for the case when the sources of the gravitational field are dust-like matter and a magnetic field. A magnetic field is orientated along a direction orthogonal to transitivity hypersurface. The solutions contain arbitrary functions. In the case of transitivity hypersurface of positive curvature and in the absence of a magnetic field, the solution is reduced to the Tolman spherically symmetric solution for dust-like matter. The conditions are studied under which the solutions with a magnetic field become asymptotically isotropic and approach the flat and the open Friedmann models. The case of transitivity hypersurfaces with signature (+ –) is also considered.