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addition angular momentum angular velocity approximation assume assumption axial symmetry axis becomes BEGIN behavior boundary values centrifugal force choose Collapse According collapsing body comoving coordinate system component of Eq corresponds critical ratio curve develop Doctor of Philosophy domain of determinacy dynamical singularity Einstein field equations equation of motion expulsion of matter fact finite function galaxies geodesic given by Eq gives gravitational collapse gravitational constant gravitational force gravitational potential energy gravitational waves hyperplane of symmetry initial value inner characteristic light rays lowest order metric momentum per unit negligible Newtonian potential Newtonian theory obtain plane of symmetry pressure gradients propagation quantities radial radius region relativistic represents repulsion require restrict result rotating body rotational kinetic energy rotational velocity seen slopes spacelike spatial spherically symmetric Substituting Eq thin disk timelike transformation triad uniform density spheroid uniform rotation unit mass vanishes vector weak field limit