Isotropic cases of static charged fluid spheres in general relativity

TL;DR

This paper derives analytical solutions for static charged fluid spheres in general relativity, matching interior solutions to exterior Reissner-Nordström metrics, and explores their relevance to compact stars.

Contribution

It presents new analytical solutions for isotropic static charged fluid spheres and connects these solutions to realistic models of compact stars.

Findings

Solutions match Reissner-Nordström exterior metrics

Derived pressure and density profiles at the center and boundary

Charged fluid spheres can model compact stars effectively

Abstract

In this paper we study the isotropic cases of static charged fluid spheres in general relativity. For this purpose we consider two different specialization and under these we solve the Einstein-Maxwell field equations in isotropic coordinates. The analytical solutions thus we obtained are matched to the exterior Reissner-Nordstr\"om solutions which concern with the values for the metric coefficients $e^{\nu}$ and $e^{\mu}$. We derive the pressure, density, pressure-to-density ratio at the centre of the charged fluid sphere and boundary $R$ of the star. Our conclusion is that static charged fluid spheres provide a good connection to compact stars.