THE MAGNETIC WEYL TENSOR AND THE VAN STOCKUM SOLUTION

Rotation is believed to be one of the sources of the magnetic part of the Weyl tenser H-ab. To test this hypothesis I study H-ab for the van Stockum metric, which refers to an infinite cylinder of rotating dust. It turns out that H-ab is non-zero inside the cylinder. In the exterior H-ab can be made to vanish for cylinders of low mass per unit length, but not for those of higher mass per unit length; this agrees with previous work which suggested that in the former case the exterior field is static.