# All static spherically symmetric anisotropic solutions for general relativistic polytropes

## TL;DR

This paper develops an algorithm to generate all static, spherically symmetric anisotropic solutions for relativistic polytropes, simplifying the process by requiring only one function, and recovers known solutions as examples.

## Contribution

It introduces a novel algorithm that constructs all such solutions using only one generating function, extending previous methods to anisotropic cases.

## Key findings

- The algorithm successfully reproduces known solutions.
- It simplifies the process of finding anisotropic solutions.
- Provides a systematic way to explore relativistic polytropic models.

## Abstract

An algorithm presented by K. Lake to obtain all static spherically symmetric perfect fluid solutions was recently extended by L. Herrera to the interesting case of locally anisotropic fluids (principal stresses unequal). In this work we develop an algorithm to construct all static spherically symmetric anisotropic solutions for general relativistic polytropes. Again the formalism requires the knowledge of only one function (instead of two) to generate all possible solutions. To illustrate the method some known cases are recovered.