A relativistic algorithm with isotropic coordinates

TL;DR

This paper introduces a new algorithm for generating exact solutions to Einstein's field equations in spherically symmetric spacetimes with isotropic pressures, utilizing isotropic coordinates and nonlinear Bernoulli equations.

Contribution

The authors develop an innovative algorithm that produces new solutions from known ones, specifically tailored for isotropic pressure distributions in relativistic models.

Findings

Derived new exact solutions for spherically symmetric spacetimes

Expressed integrals in elementary functions using conformally flat metrics

Utilized isotropic coordinates for the first time in this context

Abstract

We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a new solution if a particular solution is known. The algorithm leads to a nonlinear Bernoulli equation which can be integrated in terms of arbitrary functions. We use a conformally flat metric to show that the integrals may be expressed in terms of elementary functions. It is important to note that we utilise isotropic coordinates unlike other treatments.