Static solutions of Einstein's field equations for compact stellar objects

Abstract

In this work, we present two solutions of Einstein's field equations for compact stellar objects such as quark or neutron stars. Due to their unique stellar properties, these compact objects pose as excellent laboratories to study matter in the most extreme conditions. In part one of this paper, we solve Einstein's field equations modified for a finite value for the cosmological constant for spherically symmetric mass distributions. This solution has been presented in the literature before, but with inconsistent results. In part two, we examine the structure of deformed (non-spherical) compact objects. The stellar structure equations are derived and solved for in the limiting case of isotropic pressure and energy-density. We calculate stellar properties such as masses and radii along with pressure and density profiles for these deformed objects and investigate changes from the standard spherical models.