Relativistic Compact Objects in Isotropic Coordinates

TL;DR

This paper introduces a matrix method to derive new exact solutions for Einstein's equations describing static perfect fluid spheres, focusing on a class with a linear barotropic equation of state.

Contribution

A novel matrix transformation approach reduces Einstein's equations to Riccati equations, enabling the discovery of new classes of solutions for static perfect fluid spheres.

Findings

Derived three classes of solutions for Einstein's equations

Detailed analysis of solutions with linear barotropic equation of state

Provided explicit solutions for static perfect fluid spheres

Abstract

We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type fluid with an equation of state $p=\gamma \rho $ is discussed in detail.