Modelling anisotropic fluid spheres in general relativity

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.

V1: 6 pages; V2: now 7 pages; 7 references added; no physics changes; V3: Revised and reformatted; now 15 pages in World Scientific style. Some extra discussion added. 5 more references added. This version accepted for publication in IJMPD

References in corpus (16)

• All static spherically symmetric anisotropic solutions of Einstein's equations
• Energy conditions in the epoch of galaxy formation
• Non-radial oscillations of anisotropic neutron stars in the Cowling approximation
• Generating static spherically symmetric anisotropic solutions of Einstein's equations from isotropic Newtonian solutions
• Solution generating theorems for the TOV equation
• Anisotropic Models for Globular Clusters, Galactic Bulges and Dark Halos
• Analytical families of 2-component anisotropic polytropes and their relativistic extensions
• Anisotropic pressure and hyperons in neutron stars
• Buchdahl-like transformations for perfect fluid spheres
• Modeling usual and unusual anisotropic spheres
• Transforming the Einstein static Universe into physically acceptable static fluid spheres
• Evolving spheres of shear-free anisotropic fluid
• If vacuum energy can be negative, why is mass always positive?: Uses of the subdominant trace energy condition
• Generating Static Fluid Spheres by Conformal Transformations
• Transforming the Einstein static Universe into physically acceptable static fluid spheres II: A two - fold infinity of exact solutions
• Solution generating theorems for perfect fluid spheres

Cited by in corpus (11)

• The Kiselev black hole is neither perfect fluid, nor is it quintessence
• Nonsingular Black Holes in $f(R)$ Theories
• Charged anisotropic compact objects by gravitational decoupling
• Orbital fingerprints of ultralight scalar fields around black holes
• Decomposition of total stress-energy for the generalised Kiselev black hole
• Tidal forces in dirty black hole spacetimes
• Killing horizons and surface gravities for a well-behaved three-function generalisation of the Kerr spacetime
• Shadows of a generic class of spherically symmetric, static spacetimes
• Positivity Conditions for Generalised Schwarzschild Space-Times
• Matter environments around black holes: geodesics, light rings, and ultracompact configurations
• The spacetime geodesy of perfect fluid spheres