New anisotropic models from isotropic solutions

TL;DR

This paper presents an algorithm to generate new anisotropic solutions to Einstein's equations from known isotropic solutions, enabling easier analysis of complex astrophysical models.

Contribution

It introduces a novel method to derive anisotropic solutions from isotropic seed solutions using integral-based formulas, with explicit examples in closed form.

Findings

Generated anisotropic isothermal spheres in closed form

Produced anisotropic constant density Schwarzschild spheres

Demonstrated the method's applicability to physically relevant models

Abstract

We establish an algorithm that produces a new solution to the Einstein field equations, with an anisotropic matter distribution, from a given seed isotropic solution. The new solution is expressed in terms of integrals of known functions, and the integration can be completed in principle. The applicability of this technique is demonstrated by generating anisotropic isothermal spheres and anisotropic constant density Schwarzschild spheres. Both of these solutions are expressed in closed form in terms of elementary functions, and this facilitates physical analysis.