Properties of static fluid cylinders and plane layers in general relativity

Exact solutions of field equations representing static perfect fluid cylinders and plane layers, with possible inclusion of electromagnetic or scalar field, are constructed and discussed. For the case of cylindrical symmetry, conditions at a regular axis are formulated and examples of regular solutions are presented. For planar and pseudoplanar configurations some limitations are obtained concerning existence of mirror symmetry in the thickness direction. These limitations make such symmetry rather unprobable, thus giving evidence that realistic models for equilibrium disklike configurations should be nonstatic (rotating). A configuration described by Teixeira, Wolk, and Som, possessing planar plus mirror symmetry (the case of disordered radiation), is shown to be unphysical.