Conformally flat anisotropic spheres in general relativity

TL;DR

This paper derives new conformally flat solutions for anisotropic spheres in general relativity by integrating the Weyl tensor condition, and compares their evolution with non-flat models to highlight the Weyl tensor's role.

Contribution

It provides novel conformally flat interior solutions for anisotropic fluids in Einstein's equations and analyzes their collapse behavior.

Findings

Conformally flat solutions are explicitly constructed.

Weyl tensor influences collapse dynamics.

Anisotropy and inhomogeneity affect evolution differently.

Abstract

The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic fluids. The slow evolution of these models is contrasted with the evolution of models with similar energy density or radial pressure distribution but non-vanishing Weyl tensor, thereby bringing out the different role played by the Weyl tensor, the local anisotropy of pressure and the inhomogeneity of the energy density in the collapse of relativistic spheres.