共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we introduce Bäcklund transformation of a null Cartan curve in Minkowski 3-space as a transformation which maps a null Cartan helix to another null Cartan helix, congruent to the given one. We also give the sufficient conditions for a transformation between two null Cartan curves in the Minkowski 3-space such that these curves have equal constant torsions. By using the Da Rios vortex filament equation, based on localized induction approximation, we derive the vortex filament equation for a null Cartan curve and obtain evolution equation for it’s torsion. As an application, we show that Cartan’s frame vectors generate new solutions of the Da Rios vortex filament equation. 相似文献
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The possibility of describing null electromagnetic fields by purely metric concepts has recently been subject to some doubt. Following a method devised by Hlavatý, we here investigate the relations that a Riemannian manifold must satisfy in order to correspond to a null electromagnetic field. It is shown that in most cases the fulfilment of five geometrical relations is a necessary and sufficient condition for the existence of a null electromagnetic field. The latter is unique, except for an arbitrary constant phase factor (as in the case of non-null fields). However, in some exceptional cases, there is a larger degree of arbitrariness in the null electromagnetic field that corresponds to a given metric. Such fields (which always possess wave fronts) are not reducible to metric concepts. We then turn to examine how it can occur that null electromagnetic fields require the fulfilment of five relations, rather than three, as non-null ones. In order to settle this question, we make an attempt to consider null fields as a limiting case of non-null ones, by superimposing an arbitrary infinitesimal non-null field on a finite null one. It is then shown that the Rainich vector of such a field does not have a well defined limit, when the perturbing non-null field tends to zero. It is thereby inferred that null electromagnetic fields really have a special status within the frame of geometrodynamics. 相似文献
4.
An inverse problem of deriving the concept of quantized fields from a certain observable conserved current is investigated. It is found that a natural framework in which to attack the problem is provided for by what we shall call Green's ansatz of null decomposition of the current. The null decomposition naturally yields a set ofcolored null flags hoisted at each space-time point, a null flag comprizing a real null vector and an associated real null six-vector, and is invariant under all permutations of colors. From the fact that to any null flag there corresponds a two-component spinor it follows that the color permutation group is extended tocolor groups O(p) orU(p), wherep is the number of null flags considered. It is shown that para-Weyl (para-Fermi) fields of orderp2 can be deduced from the (chiral) set ofp colored null flags, and that the color groupU(p) is singled out that functions as the gauge group of para-Fermi theory. 相似文献
5.
The degenerate nature of the metric on null hypersurfaces makes it difficult to define a covariant derivative on null submanifolds.
Recent approaches using decomposition to define a covariant derivative on null hypersurfaces are investigated, with examples
demonstrating the limitations of the methods. Motivated by Geroch’s work on asymptotically flat spacetimes, conformal transformations
are used to construct a covariant derivative on null hypersurfaces, and a condition on the Ricci tensor is given to determine
when this construction can be used. Several examples are given, including the construction of a covariant derivative operator
for the class of spherically symmetric hypersurfaces. 相似文献
6.
Hsiang-Chuan Tsai 《Journal of sound and vibration》2010,329(18):3744-3758
The exact dynamic analysis of plane frames should consider the effect of mass distribution in beam elements, which can be achieved by using the dynamic stiffness method. Solving for the natural frequencies and mode shapes from the dynamic stiffness matrix is a nonlinear eigenproblem. The Wittrick-Williams algorithm is a reliable tool to identify the natural frequencies. A deflated matrix method to determine the mode shapes is presented. The dynamic stiffness matrix may create some null modes in which the joints of beam elements have null deformation. Adding an interior node at the middle of beam elements can eliminate the null modes of flexural vibration, but does not eliminate the null modes of axial vibration. A force equilibrium approach to solve for the null modes of axial vibration is presented. Orthogonal conditions of vibration modes in the Bernoulli-Euler plane frames, which are required in solving the transient response, are theoretically derived. The decoupling process for the vibration modes of the same natural frequency is also presented. 相似文献
7.
S. Bonanos 《General Relativity and Gravitation》1989,21(9):953-957
Given four distinct real null directions, a unique (up to a choice between three alternatives) null frame is defined geometrically. When the assumption is made that the four given null directions are the principal null directions of a Petrov type-I space-time, it is shown that the geometrically defined frame coincides with the Weyl canonical frame. 相似文献
8.
M. M. Som M. P. Martins A. Banerjee 《International Journal of Theoretical Physics》1983,22(3):237-241
A class of conformally flat solutions for null electromagnetic field is presented. Explicit forms of the field tensors are also given. The null field is characterized by shear-free, twist-free, expansion-free, and geodetic null congruences. 相似文献
9.
The cross-ratios do not uniquely fix the class of conformally equivalent configurations of null polygons. In view of applications to Wilson loops and scattering amplitudes we characterise all conformal classes of null hexagon configurations belonging to given points in cross-ratio space. At first this is done for the ordered set of vertices. Including the edges, we then investigate the equivalence classes under conformal transformations for null hexagons. This is done both for the set of null hexagons closed in finite domains of Minkowski space as well as for the set including those closed via infinity. 相似文献
10.
G. F. Torres Del Castillo 《General Relativity and Gravitation》1984,16(9):831-834
A procedure for obtaining solutions to Dirac's equation in algebraically special space-times which admit a shear-free congruence of null geodesies along the repeated principal null direction of the Weyl tensor, is presented. By aligning one of the Dirac spinors to the congruence the problem is reduced to solving one second-order linear partial differential equation for a scalar potential. The solution of the massless field equations for null fields of arbitrary spin s>1/2 aligned to the congruence is also given. 相似文献
11.
R. Penrose 《General Relativity and Gravitation》1980,12(3):225-264
A form of initial value problem is considered in which the initial hypersurface is not spacelike but null. This approach has the striking advantage over the more usual Cauchy problem that all constraints (initial data equations) are eliminated from the theory, for a wide class of interacting fields in special relativity and also for general relativity. The theory is most naturally described in terms of the two-component spinor calculus, for which an elementary introduction is given here. A general scheme for interacting fields, which holds both in special and general relativity, is presented which describes all fields in terms of sets of irreducible spinors. The concept of an exact set of such spinors is introduced and it is shown that this concept is the appropriate one for an initial value problem on a null cone without constraints. The initial data can be expressed in the form of a complex number, called a null datum, defined at each point of the null cone, one corresponding to each spinor. There is the curious feature of these null data that apparently it is sufficient here, to have onehalf as much information per point as in the corresponding Cauchy problem. The classical Maxwell-Dirac theory and the Einstein-Maxwell theory are two examples that can be put into the form of exact sets. The Einstein empty-space equations are also of particular note, and in this case the null datum describes essentially the intrinsic geometry of the null cone. The argument given here as applied to a general exact set is incomplete in two important respects. Firstly it depends on the null data being analytic, and secondly the initial hypersurface must be a cone. However, both these restrictions are removed in the case of certain elementary fields called basic free fields, examples of which are the Weyl neutrino field, the free Maxwell field, and the linearized gravitational field. For these cases a simple explicit formula is introduced which expresses the field at any point in terms of the null datum, as an integral taken over the intersection of the initial null hypersurface with the null cone of the point.This article originally appeared in 1963 in Aerospace Research Laboratories 63-56 (P.G. Bergmann). It is an important and oft-cited work, but as it has never been published in a widely distributed journal, it is generally inaccessable to the relativity community. This regrettable situation is hereby rectified-Ed.This work was done while the author was at Princeton, Syracuse, and Cornell Universities, visiting under a NATO Fellowship administered by the Department of Scientific and Industrial Research in London. The work at Syracuse was supported by the Aeronautical Research Laboratory and at Cornell by the National Science Foundation. 相似文献
12.
Parthapratim Pradhan 《Physics letters. A》2011,375(3):474-479
Circular null geodesic orbits, in extremal Reissner-Nordstrom spacetime, are examined with regard to their stability, and compared with similar orbits in the near-extremal situation. Extremization of the effective potential for null circular orbits shows the existence of a stable circular geodesic in the extremal spacetime, precisely on the event horizon which coincides with the null geodesic generator. Such a null orbit on the horizon is also indicated by the global minimum of the effective potential for circular timelike orbits. This type of geodesic is of course absent in the corresponding near-extremal spacetime, as we show here, testifying to differences between the extremal limit of a generic RN spacetime and the exactly extremal geometry. 相似文献
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Null isotropy in a spacetime is defined. The relation of null isotropy to the constant curvature and infinitesimal spatial
isotropy is investigated. The influence of null isotropy on conjugate points along null geodesics and curvature singularities
is investigated. 相似文献
15.
Samad Khakshournia 《General Relativity and Gravitation》2010,42(2):381-385
In this work the matching of a LTB interior solution representing dust matter to the Vaidya exterior solution describing null
fluid through a null hypersurface is studied. Different cases in which one is able to smoothly match these two solutions to
Einstein equations along a null hypesurface are discussed. 相似文献
16.
《Physics letters. A》1988,126(4):229-232
The analytic extension of the globally regular space-time metric for a Schwarzschild black hole is realized by a Kruskal-like coordinate transformation. The junction conditions on null hypersurface are discussed. The reason why a stable black hole bounded with null hypersurface can exist is explained. 相似文献
17.
B. O. J. Tupper 《International Journal of Theoretical Physics》1974,9(1):69-74
Solutions of the Einstein-Maxwell equations with the addition of terms representing charged null fluid emitting from a spherically symmetric body are found. One type of solution is a simple extension of that found by Bonnor and Vaidya while the other represents a null electromagnetic field with null electric current. 相似文献
18.
《Physics letters. A》2014,378(14-15):1010-1016
The null surfaces of null curves on 3-null cone have the applications in the studying of horizon types. Via the pseudo-scalar product and Frenet equations, the differential geometry of null curves on 3-null cone is obtained. In the local sense, the curvature describes the contact of submanifolds with pseudo-spheres. We introduce the geometric properties of the curvatures and show the singularities of null surfaces, which are constructed over the null curves. 相似文献
19.
Despite the elegant formulations of Kundt and Thompson[1], and Robinson and Schild[2], it is not obvious how general the generalized GoldbergSachs theorem[3] really is. A spacetime satisfying Einstein's equations with a null fluid source, for example, can elude the generalized theorem if, and only if, the null direction of the fluid is a fourfold repeated principal null direction of the Weyl tensor. An example of such a spacetime is presented. 相似文献