A class of spherically symmetric solutions with conformal killing vectors

Abstract

Spherically symmetric solutions with a conformal Killing vector in the (r, t) surface allow the null geodesics to be found with relative ease. Knowledge of the null geodesics is essential to calculating the optical properties of a solution via the optical scalar equations. Solutions of this type may be useful for the treatment of the optical properties of an inhomogeneous universe. We first address the question of whether the large class of spherically symmetric solutions found by McVittie possess conformal symmetry. We also investigate the potential for using conformal Killing vectors to aid in the solution of Einstein's Field Equations.