Modelling anisotropic fluid spheres in general relativity

TL;DR

This paper demonstrates that static anisotropic fluid spheres in general relativity can be modeled using simple classical matter components, providing a way to mimic a wide range of spherically symmetric spacetimes.

Contribution

It introduces a minimal, unique decomposition of anisotropic fluids into classical matter fields and relates energy conditions and charge distributions within this framework.

Findings

Anisotropic spheres can be modeled by perfect fluids, electromagnetic, and scalar fields.

Energy conditions for anisotropic fluids can be translated to component conditions.

The model ensures internal equilibrium via a generalized TOV equation.

Abstract

We argue that an arbitrary general relativistic static anisotropic fluid sphere, (static and spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully mimicked by suitable linear combinations of theoretically attractive and quite simple classical matter: a classical (charged) isotropic perfect fluid, a classical electromagnetic field, and a classical (minimally coupled) scalar field. While the most general decomposition is not unique, a preferred minimal decomposition can be constructed that is unique. We show how the classical energy conditions for the anisotropic fluid sphere can be related to energy conditions for the isotropic perfect fluid, electromagnetic field, and scalar field components of the model. Furthermore we show how this decomposition relates to the distribution of both electric charge density and scalar charge density throughout the model. The generalized TOV equation implies that the perfect fluid component in this model is automatically in internal equilibrium, with pressure forces, electric forces, and scalar forces balancing the gravitational pseudo-force. Consequently, we can build theoretically attractive matter models that can be used to mimic almost any static spherically symmetric spacetime.