119366478
On the symmetries of the Edgar?Ludwig metric
The conformal Killing equations for the most general (non-plane wave) conformally flat pure radiation field are solved to find the conformal Killing vectors. As expected 15 independent conformal Killing vectors exist, but in general the metric admits no Killing or homothetic vectors. However for certain special cases a one-dimensional group of homotheties or motions may exist and in one very special case, overlooked by previous investigators, a two-dimensional homethety group exists. No higher dimensional groups of motions or homotheties are admitted by these metrics.
10348027
Some restrictions on the symmetry groups of axially symmetric spacetimes
Lie transformation groups containing a one-dimensional subgroup acting cyclically on a manifold are considered. The structure of the group is found to be considerably restricted by the existence of a one-dimensional subgroup whose orbits are circles. The results proved do not depend on the dimension of the manifold nor on the existence of a metric, but merely on the fact that the Lie group acts globally on the manifold. Firstly, some results for the general case of an (m + 1)-dimensional Lie group are derived: those commutators of the associated Lie algebra involving the generator of the cyclic subgroup, X0 say, are severely restricted and, in a suitably chosen basis, take a simple form. The Jacobi identities involving X0 are then applied to show that there are further restrictions on the structure of the Lie algebra. All Lie algebras of dimensions two and three compatible with cyclic symmetry are obtained. In the two-dimensional case the group must be Abelian. For the three-dimensional case, the Bianchi type of the Lie algebra must be I, II, III, VII0, VIII or IX and furthermore in all cases the vector X0 forms part of a basis in which the algebra takes its canonical form. Finally, four-dimensional Lie algebras compatible with cyclic symmetry are considered and the results are related to the Petrov–Kruchkovich classification of all four-dimensional Lie algebras.
125608804
Note 65.39: Inverse and reciprocal functions
120435397
Irrotational perfect fluids with a purely electric Weyl tensor
All perfect fluid spacetimes with a purely electric Weyl tensor are shown to have an alignment between the fluid 4-velocity and a canonical null tetrad determined by the Weyl tensor. If, in addition, it is assumed that the flow is irrotational, the eigenframes of the shear and Weyl tensors coincide. In all but two rather special cases, it is proved that the vectors of this eigenframe are hypersurface orthogonal and consequently that a coordinate system exists in which the metric, shear and Eab (the electric part of the Weyl tensor) are all diagonal. Geodesic Petrov type D spacetimes are shown to be either Bianchi type 1 or to belong to the class of solutions considered by Szekeres (1975) and Szafron (1977). The Allnutt solutions (1982) are shown to be the only purely electric type D fields in which the shear is non-degenerate and in which the acceleration vector lies in the plane spanned by the principal null vectors. The field equations are partially integrated in two classes where no solutions are yet known.
122289003
A class of algebraically general non-null Einstein-Maxwell fields
A class of solutions of the Einstein-Maxwell field equations which satisfy the condition that the null tetrad, determined by the electromagnetic field, is parallelly transported along the curves tangent to the complex null vectors mi and mi is investigated. For the case when mi has zero twist the general solution of the field equations is found in closed form. A symmetry of the Newman-Penrose equations (1963) is used to show the relationship between this class of solutions and those recently studied by Tariq and Tupper (1974, 1975).
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.
123273188
COMPARISON OF HIGH TRANSVERSE MOMENTUM PI0 PRODUCTION FROM PI-, K-, P, AND ANTI-P BEAMS.
We compare high-transverse-momentum (P/sub perpendicular/) inclusive ..pi../sup 0/ production from ..pi../sup -/, K/sup -/, p, and p beams, at 100 and 200 GeV/c, for center-of-mass (c.m.) angles ranging from 2/sup 0/ to 115/sup 0/, and P/sub perpendicular/ .. ..pi../sup 0/X)/sigma (..pi..p ..-->.. ..pi../sup 0/X) decreases with increasing P/sub perpendicular/, and changes dramatically with c.m. angle. Also, the ratios sigma (K/sup -/p ..-->.. ..pi../sup 0/X)/sigma (..pi../sup -/p ..-->.. ..pi../sup 0/X) and sigma (pp ..-->.. ..pi../sup 0/X)/sigma (pp ..-->.. /sup 0/X) are approximately constant. The measurements are consistent with a theoretical viewpoint in which constituents of the incident hadrons undergo a hard-scattering subprocess.