118781109
Killing tensors from conformal Killing vectors
Some years ago Koutras presented a method of constructing a conformal Killing tensor from a pair of orthogonal conformal Killing vectors. When the vector associated with the conformal Killing tensor is a gradient, a Killing tensor (in general irreducible) can then be constructed. In this paper it is shown that the severe restriction of orthogonality is unnecessary and thus it is possible that many more Killing tensors can be constructed in this way. We also extend, and in one case correct, some results on Killing tensors constructed from a single conformal Killing vector. Weir's result that, for flat space, there are 84 independent conformal Killing tensors, all of which are reducible, is extended to conformally flat spacetimes. In conformally flat spacetimes it is thus possible to construct all the conformal Killing tensors and in particular all the Killing tensors (which in general will not be reducible) from conformal Killing vectors.
121708777
A class of homogeneous Einstein-Maxwell fields
The author considers solutions of the Einstein-Maxwell field equations satisfying the conditions Fij;k+lk=fFij+, Fij;k+nk=gFij+ where Fij+ is the self-dual Maxwell bivector and li and ni are the principal null vectors of Fij+. The fields are algebraically general and the most general solution is found in closed form when li and ni have non-zero twist. Several twist-free solutions are also obtained. Vacuum space-times admitting a test Maxwell field are also considered. In all cases the metric admits a three-parameter group of motions acting transitively on three-dimensional orbits. Fields satisfying the dual conditions with li and ni replaced by mi and mi are also investigated and similar results are obtained.
13652721
Irreducible Killing Tensors from Conformal Killing Vectors
Koutras has proposed some methods to construct reducible proper conformal Killing tensorsand Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformalKilling vectors exist in a given space. We give the completely general result demonstratingthat this severe restriction of orthogonality is unnecessary. In addition we correct andextend some results concerning Killing tensors constructed from a single conformal Killingvector. We give as an example a Kimura metric and demonstrate how it is possible toconstructalargerclassofreducibleproperconformalKillingtensorsandKillingtensorsthanpermitted by the Koutras algorithms. In addition, from our new result that all conformalKilling tensors are reducible in conformally ﬂat spaces, we have a method of constructingall conformal Killing tensors and hence all the Killing tensors (which will in general beirreducible) of conformally ﬂat spaces using their conformal Killing vectors.
15230558
Killing tensors and conformal Killing tensors from conformal Killing vectors
Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors.
125608804
Note 65.39: Inverse and reciprocal functions
15659787
On Stephani's rotating dust solutions
Some years ago Stephani derived two classes of rotating dust solutions. In this paper Stephani's results are generalized to the case where the cosmological constant is non-zero. The solutions are of Petrov type D and the magnetic part of the Weyl tensor vanishes. The solutions involve seven arbitrary functions of a spacelike coordinate and, in general, they admit no Killing vectors. Nevertheless the spacetime geometry is relatively simple and admits a foliation of timelike hypersurfaces of constant intrinsic curvature and zero extrinsic curvature. The (geodesic) flow-lines of the fluid are tangent to these hypersurfaces and, in general, the flow is rotating, shearing and expanding. In the vacuum limit the solutions reduce to spacetimes of constant curvature.
118861611
Observation of inclusive. omega. production at large transverse momentum
We have observed the production of ..omega.. mesons at large transverse momentum produced in 200-GeV/c pBe interactions. The ratio of inclusive production of ..omega.. to ..pi../sup 0/ at transverse momenta above 2.2 GeV/c is 0.44 +- 0.08 near x=0. The upper limit for eta' to eta production is <1.4 in the same kinematic region.