Compact anisotropic spheres with prescribed energy density

TL;DR

This paper derives new exact solutions for anisotropic spheres in Einstein's equations, generalizing previous models, with physically reasonable matter distributions and smooth matching to Schwarzschild exterior.

Contribution

It introduces a new method for generating anisotropic sphere solutions that encompass and extend prior models, ensuring physical plausibility and proper boundary conditions.

Findings

Solutions include constant and variable density models

Matter variables are physically reasonable

Models match smoothly to Schwarzschild exterior

Abstract

New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model of Maharaj and Maartens (Gen. Rel. Grav., Vol 21, 899-905, 1989) and the variable density model of Gokhroo and Mehra (Gen. Rel. Grav., Vol 26, 75-84, 1994) as special cases. These anisotropic spheres match smoothly to the Schwarzschild exterior and gravitational potentials are well behaved in the interior. A graphical analysis of the matter variables is performed which points to a physically reasonable matter distribution.