A geometric determination of the Weyl canonical frame in petrov type-I space-times

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.     

Spherically symmetric solutions of Einstein-Maxwell theory with null fluid

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.     

Null surfaces of null curves on 3-null cone

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.     

Covariant derivatives on null submanifolds

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.     

A Note on the Null Surface Formulation of GR

The purpose of this work is to study the structure and nature of the singularities of wavefronts in flat space-time. We computed the behavior at the singularities of important objects that take place in the null surface formulation of general relativity. As a secondary result we show that the Minkowski space-time with non-trivial null surfaces is a solution of the null surface approach to general relativity.     

Nonexistence of conformally flat slices in Kerr and other stationary spacetimes

It is proved that stationary solutions to the vacuum Einstein field equations with a nonvanishing angular momentum have no Cauchy slice that is maximal, conformally flat, and nonboosted. The proof is based on results coming from a certain type of asymptotic expansion near null and spatial infinity--which also show that the development of Bowen-York-type data cannot have a development admitting a smooth null infinity--and from the fact that stationary solutions do admit a smooth null infinity.     

Circular orbits in extremal Reissner-Nordstrom spacetime

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.     

Colored null flags and para-Fermi fields

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.     

On null isotropy in spacetimes

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.     

Complex null geodesics in the extended Schwarzschild universe

The generic null geodesic of the Schwarzschild–Kruskal–Szekeres geometry has a natural complexification, an elliptic curve with a cusp at the singularity. To realize that complexification as a Riemann surface without a cusp, and also to ensure conservation of energy at the singularity, requires a branched cover of the space-time over the singularity, with the geodesic being doubled as well to obtain a genus two hyperelliptic curve with an extra involution. Furthermore, the resulting space-time obtained from this branch cover has a Hamiltonian that is null geodesically complete. The full complex null geodesic can be realized in a natural complexification of the Kruskal–Szekeres metric.     

Null ellipticity in magneto-optics

We determine the relationship between the photon, cyclotron, collision and plasma frequencies which ensures a null ellipticity for electromagnetic wave propagation in a free-carrier magnetoplasma. A comparison is made with the condition for null Faraday rotation.     

On matching LTB and Vaidya spacetimes through a null hypersurface

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.     

On geometrodynamics and null fields

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.     

On Bäcklund transformation and vortex filament equation for null Cartan curve in Minkowski 3-space

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.     

Null solutions of the Yang-Mills equations

We investigate the correspondence between null solutions of the Yang-Mills equations and shearfree geodesic null congruences. We give an example of a non-Abelian null solution with twisting rays.Alexander von Humboldt Fellow. Address after 31 May 1986: Institute of Theoretical Physics, University of Warsaw, Hoa 69, 00-681 Warsaw, Poland.     

Charges as null plane integrals over tensor densities

For the purpose of defining null plane charges, densities transforming as tensors under the Lorentz group are classified as very good, good, bad and very bad. In the general case of nonconserved tensors in a theory with interaction, it is argued that, in the presence of a mass gap, null plane integrals of members of the first two classes are expected to define symmetric charge operators on dense sets of states; for the last two classes they are not. The existence of null plane charges depends on the asymptotic behavior of off mass shell scattering amplitudes. It is shown that s 1n s behavior is the maximal growth consistent with the existence of null plane charges associated with currents.Supported in part by the U.S.-Israel Binational Science Foundation (B.S.F.), Jerusalem, Israel.     

Junction conditions on null hypersurface

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.     

A new interpretation of Vaidya radiation

If Vaidya radiation is taken to be a combination of an electromagnetic energy flux together with that of a null fluid it is shown that the singularity in the current density along an axis, which arises in the absence of a null field, is removed.     

一类类光测地线的加速度

类光测地线γ0(λ)与二维类空超曲面φ正交，λ为其仿射参量.假如在类光测地线γ0(λ)上存在一点r(r=γ0(λr))共轭于类空超曲面φ，则对于γ0(λ)上任一点q(q=γ0(λq))满足λq＞λr，一定能把γ0连续变形成一条从φ到q的类时曲线.当产生类时曲线的变分矢量场不是类光测地线上的广义Jacobi场时，这些类时曲线在趋于类光测地线时，它们的固有加速度趋于无穷大. 关键词： 类光测地线 共轭点 变分