Matter-streams as sources of the Kerr metric

Abstract: An introduction to the thin-shell formalism and distributional approach to General Relativity is provided. The formalism is utilized to investigate possible distributions of matter that can act as a source to the Kerr metric. As a precursor to a collapsing surface, we recall how two counter-rotating streams of matter can be constructed to act as a source which we examine in two cases: one for a frame where the surface energy-momentum tensor is diagonal and one where the streams follow geodesics. No fully time-dependent and analytical solutions have previously been found that act as a collapsing source of the Kerr metric. We show that, for an adiabatic collapse up to first order, the surface energy-momentum tensor is incompatible with geodesic streams of matter and that diagonalizing it results in complex parameters for gravitational collapse.