  Seven new solutions to the interior static and spherically symmetric
Einstein's field equations (EFE) are found and investigated. These new
solutions are a generalisation of the quadratic density fall-off profile of the
Tolman VII solution. The generalisation involves the addition of anisotropic
pressures and electric charge to the density profile. Of these new solutions
three are found to obey all the necessary conditions of physical acceptability,
including linear stability under radial perturbations, and causality of the
speed of pressure waves inside the object. Additionally an equation of state
can be found for all the physically viable solutions. The generalised pulsation
equation for interior solutions to the EFE that include both electric charge
and pressure anisotropy is derived and used to determine the stability of the
solutions. However the pulsation equation found is general and can be used for
all new solutions that contain these ingredients.

General Relativity and Quantum Cosmology