Possible Physical Realizations of the Tolman VII solution

TL;DR

This paper reexamines the Tolman VII solution, deriving a new equation of state that models compact stars realistically, consistent with recent neutron star measurements, and satisfies stability and causality constraints.

Contribution

The paper derives a closed-form equation of state for the Tolman VII solution, enabling realistic modeling of compact stars with new physical insights.

Findings

The EOS allows modeling of neutron stars consistent with observations.

Causality and stability conditions are satisfied by the model.

Self-bound crust solutions are possible within the model.

Abstract

The Tolman VII solution (an exact static spherically symmetric perfect fluid solution) to the Einstein equations is reexamined, and a closed form equation of state (EOS) is deduced for the first time. This EOS allows further analysis leading to a viable model for compact stars to be obtained. Explicit application of causality conditions places further constraints on the model, and recent measurements of masses and radii of neutron stars prove to be within the predictions of the model. It is found that the adiabatic index ${\gamma} \geq 2$, and self-bound crust solutions are not excluded. The solution is also shown to obey known stability criteria. It is argued that this solution provides realistic limits on models of compact stars.