Generating anisotropic models for relativistic stellar objects

TL;DR

This paper develops new theorems in General Relativity to generate anisotropic, static, spherically symmetric solutions, providing novel models for the interior structure of compact stars with detailed geometric and thermodynamic analysis.

Contribution

It introduces a new class of generating theorems for Einstein's equations, leading to novel anisotropic stellar models that include known solutions as special cases.

Findings

Derived solutions serve as new models for compact star interiors.

Some solutions include well-known spacetimes as special cases.

Analyzed the constant-density solution as an incompressible limit.

Abstract

We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models for the interiors of compact stars. Their geometric and thermodynamic properties are studied in detail, and we show that some of the new spacetimes contain, as particular cases, other well-known solutions. Focusing on a constant-density solution, we assess the relevance of the newly found geometry as a candidate for the incompressible limit of anisotropic compact stellar objects, comparing its features with those of the Bowers-Liang spacetime.