Exact Solutions for Compact Objects in General Relativity
Abstract
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.
Description
Keywords
Physics, Astronomy and Astrophysics
Citation
Raghoonundun, A. M. (2016). Exact Solutions for Compact Objects in General Relativity (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/26010