Regular and Black Hole Skyrmions with Axisymmetry

It has been known that a B=2 skyrmion is axially symmetric. We consider the Skyrme model coupled to gravity and obtain static axially symmetric regular and black hole solutions numerically. Computing the energy density of the skyrmion, we discuss the effect of gravity to the energy density and baryon density of the skyrmion.     

The axially symmetric non-rotating vacuum solutions of Rosen's equations

It is shown that all axially symmetric non-rotating solutions of Rosen's field equations can be expressed in terms of two harmonic functions as well as that the total energy of Rosen's metric isMc ².     

Axisymmetric vacuum fields in general projective relativity

A method has been derived which enables one to obtain solutions to the stationary, axially symmetric vacuum fields in general projective relativity developed by Arcidiacono from known solutions of the vacuum field in Einstein's theory. The analogue of the Kerr solution in general projective relativity has been obtained as an example. Finally, a relation between the stationary and static axially symmetric vacuum fields in general projective relativity has been derived.     

One-soliton solutions from Laplace’s seed

One-soliton solutions of axially symmetric vacuum Einstein field equations are presented in this paper. Two sets of Laplace’s solutions are used as seed and it is shown that the derived solutions reduce to some already known solutions when the constants are properly adjusted. An analysis of the solutions in terms of the Ernst potential is also presented. It is found that the solutions do not reduce to the Euclidean form at spatial infinity. However, in the static limit, Weyl solutions are obtained for half integral ∂-values.     

On axially symmetric solutions to the Higgs-Kibble-Yang-Mills field equations

The field equations for axially symmetric generalizations of the 't Hooft-Polyakov magnetic monopole are written out in a preferred coordinate system. It is argued that no soliton solutions exist when the product 2eg of the electric chargee with the magnetic chargeg is an even integer.Dedicated to Achille Papapetrou on the occasion of his retirement.     

Gravitational field with toroidal topology

The Weyl formalism for static, axially symmetric solutions to Einstein's equations is employed to examine solutions of Einstein's equations with toroidal topology. We investigate a particular family of solutions that contain the Schwarzschild, Curzon, Bach-Weyl, and metric (also known as the Zipoy-Voorhees metric) as special cases.     

Linearization procedure for cylindrically and axially symmetric space-times

An investigation of the vacuum Einstein gravitational field equations for cylindrically and axially symmetric space-times is presented which leads to an equivalent differential system involving a simple nonlinearity only. The case when this equivalent system is linear is analyzed in detail and two methods for generating solutions of the Einstein vacuum equations are set up. As a result, in the axially symmetric case the linearity of the equivalent system characterizes completely the Kramer-Neugebauer transforms of Papapetrou line elements. Accordingly, Weyl solutions are shown to generate exhaustively both Lewis and van Stockum solutions. Analogous results are obtained also in the cylindrically symmetric case.     

Axially symmetric,uniformly rotating neutron stars in general relativity: a non-perturbative approach

The equilibrium problem for an axially symmetric, uniformly rotating, elastic solid neutron star is considered within the framework of a new formulation of relativistic elasticity. The analysis is fully relativistic and free of any assumption about the existence of a globally relaxed state of the star. Static configurations may exist only for rigid motions, and for such motions a set of six Einstein equations for six variables is proposed. Due both to the importance of elastic-solid lattices for the structure of neutron stars crusts and to the lack, up to now, of satisfactory axially symmetric perfect fluid interior solutions matching an asimpotically flat exterior, the results seem to indicate the possibility of constructing physically valid models of axially symmetric astrophysical objects in general relativity. The particular case of non-rotating axially symmetric elastic sources is also discussed.     

Dyonic String-Like Solution in a Non-Abelian Gauge Theory with Two Potentials

Axially symmetric dyon solutions of a non-Abelian gauge theory model with two potentials are sought. While seeking axially symmetric (flux tube like solutions) for the model, we stumbled upon an exact solution which represents an infinite string-like dyonic configuration with cylindrical symmetry.     

A new construction technique for exact axially symmetric static electrovac solutions of the Einstein-Maxwell equations

Coordinates adapted to the full electrostatic symmetries of a charged axially symmetric static system are constructed and applied to the coupled Einstein-Maxwell equations. A new solution is presented and the framework for general solutions is developed. The Weyl solutions g₀₀(Φ) are readily extracted from the formalism.     

Exact Solutions of the Time-Independent Axially Symmetric Schrödinger Equation

JETP Letters - The time-independent axially symmetric Schrödinger equation has been considered. Examples of two-dimensional potentials and exact solutions of the Schrödinger equation have...     

Astrophysically significant solutions of the Einstein and Einstein-Maxwell equations from the Laplace’s seed

The stationary solutions given by Amenedo and Manko generated from known solutions of Laplace’s equation as seed have been generalised to include the electromagnetic field. Further, the exterior solution of an axially symmetric rotating body with higher multipole moments and a solution corresponding to a Kerr object embedded in a gravitational field are given. We also give a method for constructing stationary vacuum solutions from static magnetovac solutions and vice versa and discuss a specific application of this method.     

Stationary axially symmetric Brans-Dicke-Maxwell fields

A method is presented which enables one to obtain solutions to the stationary axially symmetric Brans-Dicke fields coupled to source-free Maxwell fields from the solutions of the Einstein-Maxwell equations in Einstein's theory. The Brans-Dicke analog of the Kerr-Newman solution has been obtained as an example.     

Static and stationary solutions of the Einstein-Maxwell equations

The Weyl axially symmetric electrovac formalism for coincident gravitational and electrostatic equipotential surfaces is used to generate charged versions of some axially symmetric vacuum fields. The metric for two separated charged Curzon particles held in equilibrium by a strut is found and the condition for the removal of the strut is discussed. Kinnersley transformations applied to the two-particle metric yield spin but line singularities invariably appear along the symmetry axis and the metric is asymptotically NUT-like. It is shown that any Kinnersley transformation applied to a static axially symmetric asymptotically flat vacuum metric generates another asymptotically flat metric only if the latter is static. Moreover, the transformed metric is always undercharged (q ²<m ²) if it is asymptotically flat. A necessary and sufficient condition for asymptotic flatness in terms of the relevant parameters is found. A generalization of the Kinnersley transformation scheme is presented and illustrated by an example.     

轴对称谐振势阱中玻色凝聚气体基态和单涡旋态解

对囚禁在轴对称谐振势阱中的玻色凝聚气体，提出一种新的试探波函数，运用Gross-Pitaevskii(G-P)平均场能量泛函和变分的方法，得到玻色凝聚气体基态和单涡旋态波函数的解析表达式，并计算出凝聚原子的平均能量、原子云轴向和径向尺度比，以及产生单涡旋态的临界角速度等重要物理量与凝聚原子数N之间的关系.其结果与Dalfovo等人直接数值求解G-P方程所得到的结果相一致. 关键词： 玻色凝聚气体 G-P泛函 波函数 谐振势阱     

Stationary gravitational fields from static fields

In this note it is shown that the method of Misra and Pandey for generating stationary axially symmetric fields from static ones can only give rise to a class of solutions already known.     

Sphalerons,antisphalerons and vortex rings

We present new classical solutions of Weinberg–Salam theory in the limit of vanishing weak mixing angle. In these static axially symmetric solutions, the Higgs field vanishes either on isolated points on the symmetry axis, or on rings centered around the symmetry axis. The solutions represent systems of sphalerons, antisphalerons, and vortex rings.     

Monopole-antimonopole solutions of einstein-yang-mills-higgs theory

We construct static axially symmetric solutions of SU(2) Einstein-Yang-Mills-Higgs theory in the topologically trivial sector, representing gravitating monopole-antimonopole pairs, linked to the Bartnik-McKinnon solutions.     

Yang-Mills-Higgs monopole solutions of arbitrary topological charge

We propose a construction of static magnetic Yang-Mills-Higgs monopole solutions of arbitrary topological charge. They are axially symmetric and contain no free parameters except for their position. The regularity of the solutions has yet be proved; doing so would complete the constructive proof of existence.     

Boost-rotation symmetric spacetimes – Review

Boost-rotation symmetric spacetimes are the only locally asymptotically flat axially symmetric electrovacuum spacetimes with a further symmetry that are radiative. They are realized by uniformly accelerated particles of various kinds or black holes. Their general properties are summarized. Several examples of boost-rotation symmetric solutions of the Maxwell and Einstein equations are studied: uniformly accelerated electric and magnetic multipoles, the Bonnor-Swaminarayan solutions, the C-metric and the spinning C-metric.