Scale symmetries of spherical string fluids

Metric symmetries have always played a large role in the development of exact solutions to the Einstein field equations. Often a choice of metric symmetry is made based on an assumed symmetry of the matter distribution, i.e., spherical symmetry for astrophysical objects or cylindrical symmetry for a simple string. A homothetic motion ~homothety! describes the symmetry of scale transformations, and homothetic symmetry has been called ‘‘similarity of the first kind’’ by Cahill and Taub. One must distinguish between geometrical and physical self-similarity. Geometrical similarity is a property of the space–time metric, whereas physical similarity is a property of the matter fields. These need not be equivalent and the relationship between them also depends on the nature of the matter. Yavuz and Yilmaz recently investigated inheritance symmetries wherein the stress energy inherits metric symmetries of the type