Oppenheimer-Snyder Collapse in the BSSN Formalism

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.

Name thesis:degree_name

Bachelor

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Physics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2025

Author dc:creator

• Leonard, Aidan J.

Advisor dc:contributor.advisor

• Hughes, Scott A.

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/159940

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/159940