SELF-SIMILAR SYMMETRY IN GENERAL-RELATIVITY

Self-similar symmetry in relativity generalizes the notion of similarity of classical hydrodynamics. This symmetry is more general than homothetic Killing symmetry and conformal Killing symmetry. This paper presents a simple covariant characterization of self-similarity, for the case of spherical distributions of matter. The matter is represented by a general viscous fluid with non-vanishing shear and no heat conduction. The characterization applies to self-similarity of the type one as well as of type two, and extends previous reaults in the literature. The shear-free case is also discussed.