Regular models with quadratic equation of state

TL;DR

This paper presents new exact solutions to the Einstein-Maxwell equations for static, spherically symmetric charged matter with a quadratic equation of state, improving physical regularity and encompassing previous models.

Contribution

The authors derive a general class of solutions with quadratic equations of state, including earlier models, and demonstrate their physical reasonableness and regularity.

Findings

Solutions are expressed in elementary functions.

Models are free of singularities at the stellar center.

The solutions include previous linear and quadratic models.

Abstract

We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein-Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.