Oppenheimer-Snyder Collapse in the BSSN Formalism
Name
leonard-aidan-bs-physics-2025-thesis.pdf
Description
Thesis PDF
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1.14 MB
Format
Adobe PDF
Checksum (MD5)
72e137c0052a7ebc152dcb5903e26fcf
Author(s)
Leonard, Aidan J.
Advisor(s)
Hughes, Scott A.
Date Issued
May 2025
Publisher
Massachusetts Institute of Technology
Abstract
In general relativity, problems with high degrees of symmetry often serve as illustrative simplifications of complicated scenarios. Oppenheimer-Snyder collapse, an exact solution for the gravitational collapse of a uniform, pressure-less ball of dust into a black hole, provides valuable insight into the collapse of realistic mass distributions such as stars. Early numerical relativity simulations demonstrated that a rotating ball of dust collapses into a Kerr black hole. In this thesis, we formulate the collapse of a slowly rotating dust-ball using the BSSN framework from numerical relativity, with the aim of reproducing this result in a simple manner. By perturbing the Oppenheimer-Snyder solution in isotropic coordinates, we find semi-analytic solutions to the constraint equations at linear order in angular momentum. In addition, we develop a Mathematica simulation code for modeling of spherical vacuum systems using the BSSN formalism. Diagnostics provide comparison of our results with theoretical predictions for the simplified case of a stationary black hole. Further work is required to introduce matter terms and move from spherical to axial symmetry.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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