ON THE PARAMETERS OF THE LEWIS METRIC FOR THE LEWIS CLASS

The physical and geometrical meaning of the four parameters of the Lew is metric for the Lewis class are investigated. Matching this spacetim e to a completely anisotropic, rigidly rotating, fluid cylinder, we fi nd from the junction conditions that the four parameters are related t o the vorticity of the source. Furthermore, it is shown that one of th e parameters must vanish if one wishes to reduce the Lewis class to a locally static spacetime. Using the Cartan scalars it is shown that th e Lewis class does not include Minkowski as a special class globally, and that it is not locally equivalent to the Levi-Civita metric. It is also shown that, in contrast with the Weyl class, the parameter respo nsible for the vorticity appears explicitly in the expression for the Cartan scalars. Finally, to enhance our understanding of the Lewis cla ss, we analyse the van Stockum metric.