Rotating solenoidal perfect fluids of Petrov type D

We prove that aligned Petrov type D perfect fluids for which the vorticity vector is not orthogonal to the plane of repeated principal null directions and for which the magnetic part of the Weyl tensor with respect to the fluid velocity has vanishing divergence, are necessarily purely electric or locally rotationally symmetric. The LRS metrics are presented explicitly.Comment: 6 pages, no figure

Diameters of Open Star Clusters

The present paper presents a tabulation of data on all 600 Galactic open clusters for which it is presently possible to calculate linear diameters. As expected, the youngest `clusters' with ages < 15 Myr, contain a significant (greater than or equal to 20%) admixture of associations. Among intermediate-age clusters, with ages in the range 15 Myr to 1.5 Gyr, the median cluster diameter is found to increase with age. Small compact clusters are rare among objects with ages > 1.5 Gyr. Open clusters with ages > 1 Gyr appear to form what might be termed a `cluster thick disk', part of which consistst of objects that were probably captured gravitationally by the main body of the Galaxy.Comment: Astronomical Journal, in pres

Purely radiative irrotational dust spacetimes

We consider irrotational dust spacetimes in the full non-linear regime which are "purely radiative" in the sense that the gravitational field satisfies the covariant transverse conditions div(H) = div(E) = 0. Within this family we show that the Bianchi class A spatially homogeneous dust models are uniquely characterised by the condition that $H$ is diagonal in the shear-eigenframe.Comment: 6 pages, ERE 2006 conference, minor correction

The deformation complex is a homotopy invariant of a homotopy algebra

To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an explicit construction.Comment: A revised version. The final version will appear in the volume "Current Developments and Retrospectives in Lie Theory

Shear-free perfect fluids with a solenoidal electric curvature

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.Comment: 9 page

Purely radiative perfect fluids

We study `purely radiative' (div E = div H = 0) and geodesic perfect fluids with non-constant pressure and show that the Bianchi class A perfect fluids can be uniquely characterized --modulo the class of purely electric and (pseudo-)spherically symmetric universes-- as those models for which the magnetic and electric part of the Weyl tensor and the shear are simultaneously diagonalizable. For the case of constant pressure the same conclusion holds provided one also assumes that the fluid is irrotational.Comment: 12 pages, minor grammatical change

Globular Clusters and Dwarf Spheroidal Galaxies

Traditionally globular clusters and dwarf spheroidal galaxies have been distinguished by using one or more of the following criteria: (1) mass, (2) luminosity, (3) size, (4) mass-to-light ratio and (5) spread in metallicity. However, a few recently discovered objects show some overlap between the domains in parameter space that are occupied by galaxies and clusters. In the present note it is shown that ellipticity can, in some cases, be used to help distinguish between globular clusters and dwarf spheroidal galaxies.Comment: MNRAS (Letters), in pres

Shearfree perfect fluids with solenoidal magnetic curvature and a gamma-law equation of state

We show that shearfree perfect fluids obeying an equation of state p=(gamma -1) mu are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.Comment: 11 page