Nonlocal Equation of State in Anisotropic Static Fluid Spheres in General Relativity

TL;DR

This paper demonstrates the construction of physically plausible static anisotropic spherical matter configurations in general relativity using nonlocal equations of state, with applications to models of magnetized neutron stars.

Contribution

It introduces a method to generate static anisotropic solutions with nonlocal equations of state based on known density profiles, including special cases relevant to magnetars.

Findings

Feasible static anisotropic configurations with nonlocal EoS are constructed.

Constraints from junction and energy conditions are satisfied.

Special cases include configurations with vanishing radial or tangential pressures.

Abstract

We show that it is possible to obtain credible static anisotropic spherically symmetric matter configurations starting from known density profiles and satisfying a nonlocal equation of state. These particular types of equation of state describe, 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. To establish the physical plausibility of the proposed family of solutions satisfying nonlocal equation of state, we study the constraints imposed by the junction and energy conditions on these bounded matter distributions. We also show that it is possible to obtain physically plausible static anisotropic spherically symmetric matter configurations, having nonlocal equations of state\textit{,}concerning the particular cases where the radial pressure vanishes and, other where the tangential pressures vanishes. The later very particular type of relativistic sphere with vanishing tangential stresses is inspired by some of the models proposed to describe extremely magnetized neutron stars (magnetars) during the transverse quantum collapse.