Self-gravitating spheres of anisotropic fluid in geodesic flow

TL;DR

This paper classifies and derives new solutions for self-gravitating anisotropic fluid spheres in geodesic flow, expressing fluid characteristics via a master potential and exploring various constraints and special cases.

Contribution

It introduces a unified framework using a master potential to generate and analyze new anisotropic fluid solutions in gravitational spheres.

Findings

Derived many uncharged and charged anisotropic solutions

Found conformally flat solutions and some with uniform density

Included solutions with linear relations among pressures

Abstract

The fluid models mentioned in the title are classified. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order differential equation. Different constraints are imposed on this core of relations, finding new solutions and deriving the classical results for perfect fluids and dust as particular cases. Many uncharged and charged anisotropic solutions, all conformally flat and some uniform density solutions are found. A number of solutions with linear equation among the two pressures are derived, including the case of vanishing tangential pressure.