Anisotropic Fluid Solutions to Einstein's Equations in Spherical Symmetry

Abstract

The main objective of this thesis is to develop and investigate a class of spherically symmetric solutions to Einstein's field equations for anisotropic matter distributions. This work is partially motivated by a recent theorem of Andreasson \cite{ha1}, on the upper limit of the tenuity ratio for objects possessing equations of state of the form $p_r+ 2 p_t = \Omega \rho$, where $p_r, p_t$ and $\rho$ are the radial pressure, tangential pressure and energy density, respectively and $\Omega$ is an unspecified constant characteristic parameter of the fluid. An immediate goal was to extend this theorem to the broader class of all linear barotropic equations of state. A solution generating algorithm which yields infinitely many analytical, physically reasonable, stable fluid distributions for general linear barotropes (with and without the cosmological constant $\Lambda$) is presented and analyzed. Other general aspects of spherical anisotropic matter distributions are discussed, including historically significant developments, wave propagation and stability.