Voids in static neutron stars via a second solution of the Einstein field equations

Abstract

We show that voids can exist inside neutron stars modeled as static spherically symmetric perfect fluid masses, enabled by a second massless solution of the Einstein Field Equations that produces pressure and that is physically permissible in the interior. The boundary between this interior massless solution and hadronic matter is analogous to a phase transition, in effect truncating the equation of state at a critical pressure. We exhibit the interior massless solution and apply it to a Tolman VII neutron star with a physical equation of state, and show that applicable boundary conditions are satisfied. As a result of numerical modeling, we show that void volumes corresponding to internal densities greater than $\sim5$ times the surface density are physically plausible and energetically favorable but only perturb the stellar mass, external radius, interior redshifts, and moments of inertia, making such observables not very definitive signatures. We conclude that cold neutron stars may contain these interior voids, as intriguing metric solutions of the Einstein Field Equations in classical general relativity, but the size and influence of such voids on observables can be larger for denser more compact objects (e.g., strange quark stars or black holes).