Conformal Ricci and Matter Collineations for Anisotropic Fluid

Abstract

We study the consequences of timelike and spaccelike conformal Ricci and conformal matter collineations for anisotropic fluid in the context of General Relativity. Necessary and sufficient conditions are derived for a spacetime with anisotropic fluid to admit conformal Ricci and conformal matter collineations parallel to u^a and x^a. These conditions for timelike and spacelike conformal Ricci and conformal matter collineations for anisotropic fluid reduce to the conditions of perfect fluid when the heat flux and the traceless anisotropic stress tensor vanish. Further, for $\alpha=0$ (the conformal factor), we recover the earlier results of Ricci collineations and matter collineations in each case of timelike and spacelike conformal Ricci collineations and conformal matter collineations for the perfect fluid. Thus our results give the generalization of the results already available in the literature. It is worth noticing that the conditions of conformal matter collineations can be derived from the conditions of conformal Ricci collineations or vice versa under certain constraints.