Anisotropic fluid spheres in general relativity

Abstract

We present various analytic solutions for anisotropic fluid spheres in general relativity. First we consider genralizations of the $P=\ensuremath{\alpha}\ensuremath{\rho}$ solution to the case where pressure is anisotropic, and study the effects of anisotropy on the structure of neutron stars. Next we study radiating anisotropic fluid spheres and present three classes of analytic solutions. We also study slowly rotating anisotropic fluid spheres and present two analytic solutions corresponding to the nonradiating case. One of these solutions corresponds to uniform rotation, while the other corresponds to differential rotation. We also present differential equations to be solved for slowly rotating and radiating anisotropic fluid spheres.