The NUT metric in synchronous coordinates

The NUT metric is transformed to a synchronous frame with the help of a simple straightforward method. The three-space of this frame shows no singularity in the rate-of-strain tensor (acceleration and rotation being absent by definition) and in the three-curvature. Circular orbits with θ = const ≠ π/2 are also discussed.     

General solutions for a static isotropic metric in the Brans-Dicke gravitational theory

The complete set of vacuum solutions for the metric tensor of a static spherically symmetric field is given, some of these solutions showing the remarkable feature of not agreeing-even in first order-with the classically well-known weak-field solutions of the Brans-Dicke (B.D.) equations. The existence of a particular two-parameter family of solutions raises severe doubts about the so-called Machian aspect of B.D. theory.     

Gravitational scalar-field interaction in affine metric gravitational theory

Gravitational scalar-field interaction is examined on the basis of possible effects from torsion and nonmetrical space-time within the framework of affine-metric gravitational theory; cosmological and astrophysical topics are examined as applications of the theory. Ushinskii Yaroslavl State Pedagogic Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 97–103, May, 1997.     

Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

An exact solution of Einstein’s equations representing the static gravitational field of a quasi-spherical source endowed with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the Schwarzschild solution when the quadrupole moment vanishes. The geometric properties of timelike circular orbits (including geodesics) in this spacetime are investigated. Moreover, a comparison between geodesic motion in the spacetime of a quasi-spherical source and non-geodesic motion of an extended body also endowed with both mass and mass quadrupole moment as described by Dixon’s model in the gravitational field of a Schwarzschild black hole is discussed. Certain “reciprocity relations” between the source and the particle parameters are obtained, providing a further argument in favor of the acceptability of Dixon’s model for extended bodies in general relativity.     

Perturbations of the Plebanski metric in general relativity. I. Equations for gravitational perturbations

The Plebanski metric is analyzed by means of the Newman-Penrose formalism. The components of the Weyl and Ricci tensors and the spin coefficients are calculated. These results are applied to obtain the equations of gravitational perturbations around the Plebanski metric.     

Solutions of scalar and electromagnetic wave equations in the metric of gravitational and electromagnetic waves

The wave equation for a scalar field ? and vector potentialA* are solved in the background metric of a gravitational wave. The corresponding solutions when the metric is generated by a plane electromagnetic wave, is obtained from these solutions. The solution for the scalar wave is discussed in detail. It is found that because of the interaction, two new waves are generated in the lower order approximations. One of them has the same phase dependence as the original wave while the other shows a transient character. There is no interaction when the waves are along the same direction.     

Geodesics on the ellipsoid and monodromy

After reviewing the properties of the geodesic flow on the three-dimensional ellipsoid with distinct semi-axes, we investigate the three-dimensional ellipsoid with the two middle semi-axes equal, corresponding to a Hamiltonian invariant under rotations. The system is Liouville integrable, and symmetry reduction leads to a (singular) system on a two-dimensional ellipsoid with an additional potential and with a hard billiard wall inserted in the middle coordinate plane. We show that the regular part of the image of the energy–momentum map is not simply connected and there is an isolated critical value for zero angular momentum. The singular fibre of the isolated singular value is a doubly pinched torus multiplied by a circle. This circle is not a group orbit of the symmetry group, and thus analysis of this fibre is non-trivial. Finally we show that the system has a non-trivial monodromy, and consequently does not admit single-valued globally smooth action variables.     

Acceleration of a test particle in the gravitational field of central mass with a large number of magnetic monopoles

In a Kerr－Newman－Kasuya field we have obtained expressions of the acceleration effect and also studied the special case (v^i=0). We find that in this field, the acceleration of a falling particle has both radial and transverse components. The acceleration effects of electric charge q and magnetic charge φ are also discussed, separately.     

寻找磁单极子

电和磁遍布现代社会方方面面,构成了现有大部分科学技术的基础。因此大家倾向于认为这些效应已经被充分理解,不存在基础物理层面的未解之谜。诚然,在绝大多数应用场合,这些磁电效应可以用James Clerk Maxwell 在1864 年归纳的Maxwell 方程描述。从更深的层次上,这些效应可以从量子电动力学的角度——粒子物理标准模型的一部分,得到自洽解释。该理论工作如此之好以至于它能准确给出电子磁偶极矩的前10 位有效数字。尽管如此,现有电磁学还存在一个我们所不能理解的基础问题——有关磁单极子的问题。     

The gravitational field in the wave zone I. The radiating terms of the metric tensor

We consider an asymptotically flat space-time generated by a perfect fluid source of compact spatial support. Using the de Donder gauge conditions, the Einstein equations are reduced to a new form of Poisson-type equations. A formal iterative scheme is set up to solve these equations by expanding the components of the metric tensor in powers ofc ^–1. The coefficient of each power ofc ^–1 depends on the asymptotically retarded timeu andx, y, z and satisfies a Poisson-type equation. Assuming asymptotic flatness the solution is carried out in the first orders. The results are explicit expressions of the metric up to orderc ^–4 in terms of the source functions. These expressions hold over all space-time. A further expansion in powers ofr ^–1 gives the first terms of the metric that contribute to gravitational radiation.     

On the supersymmetric solitons and monopoles

The basic results in a new trend in supersymmetry and soliton theory are presented. It is shown that the soliton expectation value of the energy operator is the mass of the soliton without quantum corrections. A new supersymmetric monopole model in three dimensions is constructed by generalization of the supersymmetric sine-Gordon model in one space dimension.     

An experimental search for cosmic monopoles

A simple search for a flux of massive cosmic monopoles predicted by the grand unified theories of strong, electromagnetic and weak interactions, was performed using an existing cosmic ray telescope of scintillation counters. The experiment was sensitive to monopoles, coming from above and underneath the earth surface, with a velocity 7 × 10^?3 < β < 0.6. An upper limit of 6 × 10^?5 monopoles per cm² sr yr (90% c.l.) su obtained.     

The classification of monopoles for the classical groups

By studying a construction of Nahm, we compute the moduli spaces of monopoles with maximal symmetry breaking at infinity forSU(N),SO(N) andSp(N); these are found to be equivalent to spaces of holomorphic maps from ₁ into flag manifolds.Research supported in part by NSERC grant A8361 and FCAR grant EQ3518     

Tetrahedral and cubic monopoles

Using a numerical implementation of the ADHMN construction, we compute the fields and energy densities of a charge three monopole with tetrahedral symmetry and a charge four monopole with octahedral symmetry. We then construct a one parameter family of spectral curves and Nahm data which represent charge four monopoles with tetrahedral symmetry, which includes the monopole with octahedral symmetry as a special case. In the moduli space approximation, this family describes a novel kind of four monopole scattering and we use our numerical scheme to construct the energy density at various times during the motion.Address from September 1995, Institute of Mathematics, University of Kent at Canterbury, Canterbury CT2 7NZ. Email: p.m.sutcliffe@ukc.ac.uk     

On the construction of monopoles for the classical groups

ForG a classical group, an equivalence is exhibited between: