Static Anisotropic Solutions to Einstein Equations with a Nonlocal Equation of State

TL;DR

This paper introduces a method to generate static, anisotropic, spherically symmetric solutions to Einstein's equations using a nonlocal equation of state, linking local properties to the entire enclosed matter configuration.

Contribution

It provides a novel approach to derive solutions with nonlocal equations of state from known density profiles, analyzing their physical viability in general relativity.

Findings

Solutions can satisfy physical acceptability conditions

Nonlocal equations of state are compatible with bounded matter distributions

Method applies to certain regions within matter configurations

Abstract

We present a general method to obtain static anisotropic spherically symmetric solutions, satisfying a nonlocal equation of state, from known density profiles. This equation of state describes, at a given point, the components of the corresponding energy-momentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. In order to establish the physical aceptability of the proposed static family of solutions satisfying nonlocal equation of state,\textit{}we study the consequences imposed by the junction and energy conditions for anisotropic fluids in bounded matter distribution. It is shown that a general relativistic spherically symmetric bounded distributions of matter, at least for certain regions, could satisfy a nonlocal equation of state.