Self-gravitating charged fluid spheres with anisotropic pressures

TL;DR

This paper derives new solutions to Einstein-Maxwell equations for charged, anisotropic fluid spheres, extending the Tolman VII model and providing explicit expressions for metric functions and pressures.

Contribution

It introduces novel exact solutions for charged, anisotropic fluid spheres in general relativity, expanding the class of models beyond previous solutions like Tolman VII.

Findings

Explicit metric functions and pressures derived for charged, anisotropic spheres.

All integration constants expressed in terms of physically meaningful parameters.

Solutions applicable to modeling realistic astrophysical objects.

Abstract

The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures which extend the Tolman VII exact solution are deduced from the new solutions. By applying boundary conditions to these solutions, all integration constants are computed in terms of parameters that are physically meaningful.