Possible Physical Realizations of the Tolman VII solution

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 $\gamma \ge 2$, 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.

Accepted and published in PRD

References in corpus (3)

• Neutron Star Observations: Prognosis for Equation of State Constraints
• Sound Speeds, Cracking and Stability of Self-Gravitating Anisotropic Compact Objects
• The Mass and Radius of the Neutron Star in 4U 1820-30

Cited by in corpus (23)

• Anisotropic Tolman VII solution by gravitational decoupling
• Improved Analytic Modeling of Neutron Star Interiors
• Convection and cracking stability of spheres in General Relativity
• Constraints on the equation of state from the stability condition of neutron stars
• Compact stars with exotic matter
• Extended Tolman III and VII solutions in $f(\mathcal{R},T)$ gravity: Models for neutron stars and supermassive stars
• Effects of the equation of state on the core-crust interface of slowly rotating neutron stars
• Acceptability Conditions and Relativistic Barotropic Equations of State
• Dynamical stability of the modified Tolman VII solution
• New interior model of neutron stars
• Neutrino trapping in extremely compact Tolman VII spacetimes
• Precursory collapse in Neutron Star-Black Hole mergers
• On the maximum compactness of neutron stars
• Slowly rotating Tolman VII solution
• Possible existence of stable compact stars in $\kappa (\mathcal{R},\mathcal{T})-$gravity
• Horizonless star based on regular black hole with finite radius and its observational signatures
• Configurational entropy and stability conditions of fermion and boson stars
• A metric on the space of neutron star models in general relativity and modified gravity
• Analytical model of millisecond pulsar PSR J0514-4002A
• Compact regular objects from an electrified Tolman-like density: A new interior region for the Kerr-Newman spacetime
• The Tolman VII Space-time in the Presence of a Charge and a Cosmological Constant
• Spherical and Plane Symmetric Solutions in Macroscopic Gravity
• Statistical complexity as a probe of mass and phase structure in compact objects