Compact anisotropic spheres with prescribed energy density
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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.