Generating static spherically symmetric anisotropic solutions of Einstein's equations from isotropic Newtonian solutions

Abstract

I use the Newtonian equation of hydrostatic equilibrium for an isotropic fluid sphere to generate exact anisotropic solutions of Einstein's equations. The input function is simply the density. An infinite number of regular solutions are constructed, some of which satisfy all the standard energy conditions. Two classes of these solutions generalize the Newtonian polytropes of index 0 and 1.