All static spherically symmetric anisotropic solutions for general relativistic polytropes

Abstract

In this work, we develop an algorithm to construct all static spherically symmetric anisotropic solutions for general relativistic polytropes. To this end, we follow the strategy presented by K. Lake in Phys. Rev. D67 (2003) 104015 to obtain all static spherically symmetric perfect fluid solutions and then extended by L. Herrera el al., Phys. Rev. D77 (2008) 027502 to the interesting case of locally anisotropic fluids. The formalism here developed requires the knowledge of only one function to generate all possible solutions. To illustrate the method, we obtain formal expressions for the generating functions of known polytopic solutions. Additionally, we obtain the generating function for both the conformally flat and class 1 polytropes.