No Go Theorem for Kinematic Self-Similarity with A Polytropic Equation of State

Abstract

We have investigated spherically symmetric spacetimes which contain a perfect fluid obeying the polytropic equation of state and admit a kinematic self-similar vector of the second kind which is neither parallel nor orthogonal to the fluid flow. We have assumed two kinds of polytropic equations of state and shown in general relativity that such spacetimes must be vacuum.Comment: 5 pages, no figures. Revtex. One word added to the title. Final version to appear in Physical Review D as a Brief Repor