# New algorithms to obtain analytical solutions of Einstein's equations in isotropic coordinates

## TL;DR

This paper introduces two novel methods inspired by the MGD approach to derive new anisotropic solutions of Einstein's equations in isotropic coordinates, demonstrating their effectiveness through four analytical solutions.

## Contribution

It presents two inequivalent algorithms for solving Einstein's equations with anisotropy in isotropic coordinates, expanding the toolkit for finding exact solutions.

## Key findings

- Four analytical solutions obtained, two are physically acceptable.
- Methods are inspired by the MGD approach in Schwarzschild coordinates.
- Demonstrates the applicability of new algorithms to generate solutions.

## Abstract

The main objective of this work, is to show two inequivalent methods to obtain new spherical symmetric solutions of Einstein's Equations with anisotropy in the pressures in isotropic coordinates. This was done inspired by the MGD method, which is known to be valid for line elements in Schwarzschild coordinates. As example, we obtained four analytical solutions using Gold III as seed solution. Two solutions, out of four, (one for each algorithm), satisfy the physical acceptability conditions.