On Slowly Rotating Supercompact Schwarzschild Stars

In this Ph.D thesis, I will present results concerning to my doctoral research project submitted to the Department of Physics and Astronomy at the University of South Carolina. The thesis belongs to the area of Theoretical Physics, particularly, in the framework of Einstein’s Theory of General Relativity.The project is the study of integral and surface properties of slowly rotating homogeneous masses in the gravastar limit R ! Rs, where Rs is the Schwarzschild radius. For this purpose we followed the perturbative method proposed by Hartle in 1967. In this model, the relativistic equations of structure for a slowly rotating star were derived at second order in the angular velocity . An interesting, and educational, application of this model was investigated by Chandrasekhar and Miller. In their approach, they solved numerically the structure equations of a homogeneous star (constant energy density) up to the Buchdahl bound (9/8)Rs. Based on this work, our objective was to investigate the interesting region below the Buchdahl bound Rs < R < (9/8)Rs, which has not been studied previously in the literature. Our results were astonishing. We found that the surface properties and quadrupole mass moment approach the values corresponding to those of the Kerr metric when expanded at second order in angular momentum. This remarkable result provides a long sought solution to the problem of the source of rotation in the Kerr spacetime.