Formalism for the rapid evolution of primordial black holes

Abstract

This thesis presents two different formalisms which can be used together to evolve a density perturbation produced during inflation forwards in time in the radiation-dominated era of the early universe. The first formalism, based on early work by Misner and Sharp, is for the evolution of a perfect fluid in spherical symmetry under its own gravity. This allows us to efficiently determine if a black hole will form, but due to the formation of a singularity, it does not allow us to extract the black hole's mass. The second, new, formalism allows us to evolve the density perturbation past the formation of a singularity until a time where we can reasonably extract the mass of the black hole. This new formalism has been designed to do this computation as rapidly as possible, improving over our previous methods. The limits of this new formalism are investigated, details regarding a numerical implementation of our code are discussed, and a proof of concept example is presented.