On Spherically Symmetric Non-Static Space-Times Admitting Homothetic Motions

Spherically symmetric solutions admitting a homothetic Killing vector field (HKVF) either orthogonal, ${\eta }_{\mathrm{\perp }}$, or parallel,${\eta }_{\mathrm{\mid }\mathrm{\mid }}$, to the 4-velocity vector field, $u^a$, are studied. New self-similar solution of Einstein’s field equation is found in the case when HKVF is in a general form. Some physical properties of the obtained solution are examined.